We describe how to construct an effective Hamiltonian for leading twist states in $d\ge 3$ CFTs based on the separation of scales that emerges at large spin $J$ between the AdS radius $\ell_{\rm AdS}$ and the characteristic distance $\sim \ell_{\rm AdS} \log J$ between particles rotating in AdS with angular momentum $J$. As a controlled example, we work specifically with the toy model of a bulk complex scalar field $\phi$ with a $\lambda |\phi|^4$ coupling in AdS, up to $O(\lambda^2)$. For a given choice of twist cutoff $\Lambda_\tau$ in the effective theory, interactions are separated into long-distance nonlocal potential terms, arising from $t$-channel exchange of states with twist $\le \Lambda_\tau$, and short-distance local terms fixed by matching to low spin CFT data. At $O(\lambda^2)$, the effective Hamiltonian for the toy model has two-body nonlocal potential terms from one-loop bulk diagrams as well as three-body nonlocal potential terms from tree-level exchange of $\phi$. We describe in detail how these contributions are evaluated and how they are related to the CFT data entering in the large spin expansion. We discuss how to apply the construction of such effective Hamiltonians for models which do not have a large central charge or a sparse spectrum and are not typically considered holographic.

We show how to construct a holographic effective theory for the leading-twist operators in the $O(2)$ model in the $4-d=\epsilon$ expansion up to $O(\epsilon^2)$, based on the separation of short-distance and long-distance effects that arises as a function of spin $J$. We obtain the Hamiltonian of the theory and show that it correctly reproduces all the dimensions at $O(\epsilon^2)$ of the leading twist operators for all values of the charge $Q$ and spin $J$. The holographic Hamiltonian is given by the bulk exchange of a charged scalar $\phi$, neutral scalar $s \sim \phi \phi^*$, and a `ghost' field $c$, as well as a single local bulk interaction $(\phi \phi^*)^2$. We analyze various aspects of the spectrum and discuss their interpretation in light of the bulk description.

We introduce a new positive geometry, the associahedral grid, which provides a geometric realization of the inverse string theory KLT kernel. It captures the full $\alpha'$-dependence of stringified amplitudes for bi-adjoint scalar $\phi^3$ theory, pions in the NLSM, and their mixed $\phi$/$\pi$ amplitudes, reducing to the corresponding field theory amplitudes in the $\alpha'\to 0$ limit. Our results demonstrate how positive geometries can be utilized beyond rational functions to capture stringy features of amplitudes, such as an infinite resonance structure. The kinematic $\delta$-shift, recently proposed to relate field theory $\text{Tr}(\phi^3)$ and NLSM pion amplitudes, naturally emerges as the leading contribution to the stringy geometry. We show how the connection between $\text{Tr}(\phi^3)$ and NLSM can be geometrized using the associahedral grid.

We consider two dimensional superconformal Carrollian theories with boundaries and construct two variants of the Boundary Superconformal Carrollian Algebra (BSCCA), viz. the Homogeneous and the Inhomogeneous, by making appropriate identification of the parent superconformal Carrollian algebras. These new algebras are then recovered by appropriate limits of a single copy of Super Virasoro algebra. We then focus on the theory of null tensionless superstrings and construct, for the first time, an open null superstring. The Homogeneous version of the BSCCA is realised as worldsheet symmetries on this open null superstring.

It was recently shown that a black hole (or any Killing horizon) will decohere any quantum superposition in their vicinity. I review three distinct but equivalent arguments that illustrate how this phenomenon arises: (1) entanglement with "degrees of freedom" in the interior (2) the absorption of soft, entangling radiation emitted by the superposition and (3) interactions with the quantum, fluctuating multipole moments of a black hole arising from ultra low frequency Hawking quanta. The relationship between "soft hair" and interactions with "internal degrees of freedom" is emphasized and some implications for the nature of horizons in a quantum theory of gravity are discussed.

Realising $F$-term slow-roll inflation in supergravity is non-trivial due to the well-known $\eta$-problem. The common strategy to solve the problem is to impose a shift symmetry on the Kähler potential, but this often leads to a negative potential in the large-field regime. To avoid negative potentials, an additional superfield called the stabiliser is usually added with a desired interaction. An alternative mechanism in supergravity, avoiding the use of a stabiliser superfield, was earlier proposed by two of us in the setup with a single chiral superfield having inflaton and goldstino amongst its field components. In this work, we extend that alternative mechanism to multi-superfield models of inflation, thereby providing a generic framework for embedding a wide class of single- and multi-field inflation models into supergravity. We illustrate our approach by several concrete examples of multi-field inflation and clarify the conditions required to avoid tachyonic instabilities during multi-field evolution. Our proposal significantly broadens the theoretical landscape of $F$-term inflation models in supergravity.

The large $N$ analysis of QCD states that the potential for the $\eta'$ meson develops cusps at $\eta' = \pi / N_f$, $3 \pi /N_f$, $\cdots$, with $N_f$ the number of flavors. Furthermore, the recent discussion of generalized anomalies tells us that even for finite $N$ there should be cusps if $N$ and $N_f$ are not coprime, as one can show that the domain wall configuration of $\eta'$ should support a Chern-Simons theory on it, i.e., domains are not smoothly connected. On the other hand, there is a supporting argument for instanton-like, smooth potentials of $\eta'$ from the analyses of softly-broken supersymmetric QCD for $N_f= N-1$, $N$, and $N+1$. We argue that the analysis of the $N_f = N$ case should be subject to the above anomaly argument, and thus there should be a cusp; while the $N_f = N \pm 1$ cases are consistent, as $N_f$ and $N$ are coprime. We discuss how this cuspy/smooth transition can be understood. For $N_f< N$, we find that the number of branches of the $\eta'$ potential is $\operatorname{gcd}(N,N_f)$, which is the minimum number allowed by the anomaly. We also discuss the condition for s-confinement in QCD-like theories, and find that in general the anomaly matching of the $\theta$ periodicity indicates that s-confinement can only be possible when $N_f$ and $N$ are coprime. The s-confinement in supersymmetric QCD at $N_f = N+1$ is a famous example, and the argument generalizes for any number of fermions in the adjoint representation.

In this paper, we develop the general formalism and properties of the spacetime density matrix, which captures correlations among different Cauchy surfaces and can be regarded as a natural generalization of the standard density matrix defined on a single Cauchy surface. We present the construction of the spacetime density matrix in general quantum systems and its representation via the Schwinger Keldysh path integral. We further introduce a super-operator framework, within which the spacetime density matrix appears as a special case, and discuss possible generalizations from this perspective. We also show that the spacetime density matrix satisfies a Liouville von Neumann type equation of motion. When considering subsystems, a reduced spacetime density matrix can be defined by tracing over complementary degrees of freedom. We study the general properties of its moments and, in particular, derive universal short time behavior of the second moment. We find that coupling between subsystems plays a crucial role in obtaining nontrivial results. Assuming weak coupling, we develop a perturbative method to compute the moments systematically.

We examine the giant graviton expansions of the Higgs indices for the 3d $\mathcal{N}=4$ $U(N)$ ADHM theories with $l$ fundamental hypermultiplets. The indices for the M5-brane giant gravitons of wrapping number $m$ appearing in the expansions consist of the contributions that generalize the characters of the W-algebra $\mathcal{W}(\mathfrak{gl}(m))$ and those which realize the characters of the affine Kac-Moody algebras of type $A_{l-1}$. Also we confirm that the inverse giant graviton expansions of the resulting M5-brane indices consistently reproduce the Higgs indices.

We study the ODE/IM correspondence for two-dimensional conformal field theories with Virasoro and $\mathcal{W}_N$ symmetry. Building on earlier work establishing the correspondence, we develop a systematic algorithm for calculating the eigenvalues of local integrals of motion in terms of the Bethe roots using formal WKB expansions of wave functions associated to the differential operators. The method is demonstrated explicitly for Virasoro, $\mathcal{W}_3$, and $\mathcal{W}_4$ algebras, yielding closed expressions for the eigenvalues of the first few local quantum KdV Hamiltonians. A key geometric structure emerging from our analysis is the mirror curve, a three-punctured sphere that is naturally covered by the WKB curve. We show how the algebraic properties of the $\mathcal{W}$-symmetry algebras are reflected in the geometry of these curves, and how period integrals on these curves reproduce the spectral data of the integrable system. Applications to Argyres-Douglas minimal models allow us to test the prescription both analytically and numerically and we find complete agreement between the calculations in different triality frames. Finally, we examine large rank limits of ground state eigenvalues and show that they match the genus expansion of the topological string partition function on $\mathbb{C}^3$.

The three-dimensional classical O($N$) model with a boundary has received renewed interest due to the discovery of the extraordinary-log boundary university class for $2\leq N< N_\text{c}$. The exponent of the spin correlator and the critical value $N_c$ are related to certain universal amplitudes in the normal universality class. To determine their precise values, we revisit the 3d O($N$) boundary conformal field theory (BCFT) for $N=1, 2, 3, 4, 5$. After substantially improving the accuracy of the boundary bootstrap, our determinations are in excellent agreement with the Monte Carlo results, resolving the previous discrepancies due to low truncation orders. We also use the recent bulk bootstrap results to derive highly accurate Ising data. Many bulk and boundary predictions are obtained for the first time. Our results demonstrate the great potential of the $\eta$ minimization method for many unexplored non-positive bootstrap problems.

We solve the classical and quantum problems for the 1D sigma model with target space the flag manifold $\mathrm{U}(3)\over \mathrm{U}(1)^3$, equipped with the most general invariant metric. In particular, we explicitly describe all geodesics in terms of elliptic functions and demonstrate that the spectrum of the Laplace-Beltrami operator may be found by solving polynomial (Bethe) equations. The main technical tool that we use is a mapping between the sigma model and a Gaudin model, which is also shown to hold in the $\mathrm{U}(n)$ case.

We study a class of observables in four-dimensional superconformal Yang--Mills theories which, in the planar limit at finite 't Hooft coupling, can be expressed as determinants of semi-infinite matrices built from Bessel functions. This determinant representation points to an underlying integrable structure, which we make explicit by showing that the observables satisfy a nonlinear differential-difference equation. We argue that the solution to this equation admits an expansion in terms of iterated Chen integrals of uniform transcendental weight. Remarkably, the coefficients in this expansion are universal positive integers, independent of the particular observable, suggesting a hidden combinatorial origin. Building on this observation, we show that the resulting expressions possess a natural interpretation in enumerative combinatorics: they coincide with the partition function (or generating function) of an ensemble of lattice paths constrained to a nontrivial domain. This correspondence extends and generalizes the classical Dyck paths to a richer family of path ensembles relevant in gauge theory.

Non-perturbative partition functions of quantum theories constitute a class of $\tau-$functions, which are distinguished satisfying Hirota's bilinear identities(BI). To make this statement general, there must be a proper definition of $\tau-$function that gives rise to a set of bilinear identities. In the classical definition of $\tau-$function for integrable Toda or KP hierarchies, there is a restriction on matrix elements to be based on group-like elements with the comultiplication $\Delta(g)=g \otimes g$. This restriction can not be straightforwardly transferred to the q-deformed case, because there are no group-like elements in q-deformed universal enveloping algebra (UEA), except for its Cartan subalgebra. The new approach to the $\tau-$function is to remove the restriction on g to be obligatory the group-like element. The main result of this work is a derivation of the set of bilinear identities and $\tau-$functions for $U_q(\mathfrak{sl}_3)$ in the fundamental representations for non-group-like elements. We consider difference operators which lead to the basic bilinear identities. Also, we provide an analysis of the ways of obtaining BI for higher rank algebras $U_q(sl_n)$.

These notes review the D0-brane or Banks-Fischler-Shenker-Susskind (BFSS) matrix quantum mechanics from a post-AdS/CFT perspective. We start from the decoupling argument for D0-branes and discuss the gravity dual in the 't Hooft regime, before extrapolating to strong coupling. In the second part of these notes, we review the matrix bootstrap method and its application to the D0-brane quantum mechanics.

We investigate the quantization of a single unstable mode in a real scalar field subject to a Robin boundary condition in (1+1)-dimensional half-Minkowski spacetime. The instability arises from an imaginary frequency mode - analogous to that of the inverted harmonic oscillator - requiring the rigged Hilbert space formalism for consistent quantization. Within this framework, the unstable mode is naturally described as a well-defined decaying (or growing) quantum state with a characteristic mean lifetime. We investigate its physical consequences via the response of an Unruh-DeWitt detector along static, inertial, and uniformly accelerated trajectories. For static and inertial observers, the detector response exhibits a Breit-Wigner resonance profile, with a decay width determined by the unstable frequency and a Doppler factor. In the Neumann limit, infrared divergences emerge from arbitrarily low-frequency modes. Interestingly, for accelerated detectors, the response acquires a nontrivial dependence on acceleration, and the Neumann limit yields a finite, oscillatory signal rather than a divergence, suggesting that acceleration can act as an effective infrared regulator.

We explore the dynamics of the fermion-rotor system, a simple impurity model in d=1+1 dimensions that consists of a collection of purely right-moving fermions interacting with a quantum mechanical rotor localised at the origin. This was first introduced by Polchinski as a toy model for monopole-fermion scattering and is surprisingly subtle, with ingoing and outgoing fermions carrying different quantum numbers. We show that the rotor acts as a twist operator in the low-energy theory, changing the quantum numbers of excitations that have previously passed through the origin to ensure scattering consistent with all symmetries. We further show how generalisations of this model with multiple rotors and unequal charges can be viewed as a UV-completion of boundary states for chiral theories, including the well-studied 3450 model. We compute correlation functions between ingoing and outgoing fermions and show that fermions dressed with the rotor degree of freedom act as local operators and create single-particle states, generalising an earlier result obtained in a theory with a single rotor and equal charges. Finally, we point out a mod 2 anomaly in these models that descends from the Witten anomaly in 4d

We introduce a new algebraic framework to describe gravitational scrambling, including the semiclassical limit of any out-of-time-order correlation function that is built out of operator insertions separated by approximately the scrambling time. In two dimensions, the scrambling algebra, which we call a modular-twisted product, is defined in terms of two copies of the Leutheusser-Liu half-sided modular inclusion of von Neumann algebras; these describe early- and late-time operators respectively. In limits where the separation between insertions is taken to be either significantly greater or smaller than the scrambling time, the modular-twisted product reduces, respectively, to free- and tensor-product algebras that were previously studied in [arXiv:2209.10454]. In a sense, the modular-twisted product interpolates between these two products. Including the Hamiltonian in the scrambling algebra leads to a Type II$_\infty$ von Neumann algebra with finite renormalized entropies that interpolate between single-QES and multi-QES phases. We also describe how to generalize the modular-twisted product algebra to higher dimensions, including spatially localized boundary excitations.

We investigate the role of framing in a family of 1/24 BPS Wilson loops in ABJ(M) theory, which define flows of supersymmetric defect field theories, interpolating between the 1/6 BPS and the 1/2 BPS superconformal fixed points. We analyze in perturbation theory how framing affects both the expectation values of these operators and the correlation functions of local insertions on the defect, as well as its interplay with RG flow and the g-theorem. We obtain a non-trivial identity between the one-point function of the defect stress tensor and a Q-exact correlator, which establishes a direct link between scale invariance, superconformal invariance and framing, and clarifies the deep connection between scale and cohomological anomalies. Finally, we propose a holographic interpretation of framing at strong coupling, identifying it with a coupling to the background B-field in the dual string theory.

We study weakly-coupled descriptions/channel decompositions of the 4d $\mathcal{N}=2$ theories of class $\mathcal{S}$ of type $\mathfrak{su}(N)$, from the perspective of the 3d $\mathcal{N}=4$ mirror duals of their circle compactifications. This is a delicate problem when the channel decomposition produces pathological, or bad, 4d configurations that correspond to spheres with non-maximal punctures. The star-shaped quivers, describing the 3d mirrors associated with such bad 4d configurations, are bad 3d $\mathcal{N}=4$ theories. Leveraging recent results regarding 3d bad theories, we identify a new and interesting family of bad theories, which we coin \textit{broken} theories, that naturally arise in this context. Using these broken theories, we develop a systematic and analytic method that determines the generically non-Lagrangian matter sectors and the weakly-coupled gauge groups in such channel decompositions. We understand these weakly-coupled descriptions as emerging dynamically via Higgs mechanisms triggered by operators acquiring vacuum expectation values.

We present a comprehensive theoretical analysis of the General Standard Model (GSM), a recently proposed framework that unifies particle physics and cosmology within the Gravitational Quantum Field Theory (GQFT). Constructed from first principles based exclusively on the intrinsic properties of leptons and quarks, the GSM reveals an enlarged gauge symmetry structure, WS$_{c}$(1,3)$\times$GS(1)$\times$Z$_2$, which extends beyond the conventional U$_Y$(1)$\times$SU$_L$(2)$\times$SU$_C$(3) symmetry of the Standard Model. Here, WS$_{c}$(1,3) = SP(1,3)$\rtimes$W$^{1,3}\rtimes$SP$_c$(1,1) emerges as the conformal inhomogeneous spin gauge symmetry. Within GQFT, the GSM provides a consistent unification of the Standard Model of particle physics with cosmological models. It incorporates the four known fundamental interactions, electromagnetic, weak, strong, and gravitational, plus the Higgs scalar interaction, and also predicts novel interactions. These include spin gauge, chirality boost-spin gauge, chiral conformal-spin gauge, and scaling gauge forces, as well as additional scalar interactions. Furthermore, the GSM offers profound insights into the nature of gravity and spacetime and elucidates key mysteries of the dark side of the universe, such as the origins of dark matter, the dynamics of dark energy, and the physics of the early inflationary epoch. By establishing a new theoretical bridge between quantum field theory and general relativity, the GSM opens novel pathways for addressing long-standing challenges in fundamental physics. It provides a unified description of both fundamental interactions and cosmic evolution.

Black holes in General Relativity exhibit a remarkable feature: their response to static scalar, electromagnetic, and gravitational perturbations -- as quantified by the so-called tidal Love numbers -- vanishes identically. We present the first exception to this rule: the Love numbers of a black hole perturbed by a fermionic field are nonzero. We derive a closed-form expression of these fermionic Love numbers for generic spin in the background of a Kerr black hole with arbitrary angular momentum. In contrast, we show that the fermionic dissipation numbers vanish for static perturbations, reflecting the absence of superradiance for fermions. These results highlight a fundamental distinction between bosonic and fermionic perturbations, which can be interpreted as a breaking of the hidden symmetries that underlie the vanishing of Love numbers in the bosonic sector.

We present a theoretical framework for the cuprate superconductors, rooted in a fractionalized Fermi liquid (FL*) description of the intermediate-temperature pseudogap phase at low doping. The FL* theory predicted hole pockets each of fractional area $p/8$ at hole doping $p$, in contrast to the area $p/4$ in a spin density wave state or its thermal fluctuation. A recent magnetotransport observation of the Yamaji angle is in good agreement with area $p/8$. We review a theory for the FL* phase of a single-band model using a pair of ancilla qubits on each site. Its mean field theory yields hole pockets of area $p/8$, and matches the gapped photoemission spectrum in the anti-nodal region of the Brillouin zone. Fluctuations are described by the SU(2) gauge theory of a background spin liquid with critical Dirac spinons. A Monte Carlo study of the thermal SU(2) gauge theory transforms the hole pockets into Fermi arcs. One route to confinement upon lowering temperature yields a $d$-wave superconductor via a Kosterlitz-Thouless transition of $h/(2e)$ vortices, with nodal Bogoliubov quasiparticles featuring anisotropic velocities and vortices surrounded by charge order halos. An alternative route produces a charge-ordered metallic state that exhibits quantum oscillations in agreement with experimental data. Increasing doping from the FL* phase drives a transition to a conventional Fermi liquid at large doping, passing through an intermediate strange metal regime. We formulate a theory of this metal using a critical quantum `charge' liquid of mobile electrons in the presence of disorder, developed via an extension of the Sachdev-Ye-Kitaev model. At low temperatures, and across optimal and over doping, we address the regimes of extended non-Fermi liquid behavior by Griffiths effects near quantum phase transitions in disordered metals.

It is well known that the noninteracting Majorana chain is dual to the one-dimensional transverse-field Ising model, either through the Jordan-Wigner transformation or by gauging fermion parity. In this correspondence, the minimal translation of the Majorana chain maps to the celebrated Kramers-Wannier (KW) duality of the spin model, with the critical point mapped to the self-dual point. In this work, we generalize this mapping to two and higher dimensions by constructing a unitary equivalence between the parity-gauged fermionic system and a spin system defined on arbitrary polyhedral decompositions of space. Imposing the flatness condition on the gauge field yields a bosonization duality between the original (ungauged) fermionic system and a gauged spin system obeying a Gauss law. The dependence of the Gauss law in the spin system on the Kasteleyn orientation (and the discrete spin structure) of the fermionic system is made explicit. Applying this bosonization to one or two copies of Majorana fermions on translationally invariant lattices, we derive higher-dimensional analogs of KW (self-)dualities in spin systems arising from fermionic minimal translations. The KW (self-)dualities are non-invertible due to projections onto eigenspaces of higher-form symmetries in the associated symmetry operators. The bosonization framework we present is intuitive, general, and systematic, encompassing other known exact bosonization methods while offering a novel approach to establish new connections between fermionic and spin systems in arbitrary dimensions.

Extreme-mass-ratio inspirals, where a stellar-mass object orbits a supermassive black hole, are prime sources of millihertz gravitational waves for upcoming space-based detectors. While most studies assume idealized vacuum backgrounds, realistic extreme-mass-ratio binaries are embedded in astrophysical environments, such as accretion disks, stellar clusters, or dark matter spikes, disks and halos, that can significantly alter the orbital dynamics. We explore bound geodesics around general-relativistic solutions describing rotating black holes surrounded by matter halos, for the first time, and map how environmental effects meddle with the spacetime symmetries of vacuum spinning (Kerr) black holes. In particular, we find that the loss of a Carter-like constant leads to geodesic non-integrability and the onset of chaos. This manifests through resonant island and chaotic layer formations around transient orbital resonances in phase space; features that are otherwise completely absent in integrable Kerr geodesics. Resonant islands, which are extended, non-zero volume regions in phase space, encapsulate periodic orbit points. Non-integrability ensures that the periodicity of the central resonant point is shared throughout the island's geodesics, thus effectively enhancing the lifespan of resonances, beyond Kerr-based predictions. Therefore, they can subject distinct imprint on gravitational-wave signals, with significant consequences for gravitational-wave modeling and parameter inference of astrophysical extreme-mass-ratio inspirals.

We investigate the impact of a uniform spin density on the critical temperature of the chiral phase transition in finite-temperature QCD in the scope of the linear sigma model. We demonstrate that at a finite spin potential $\mu_\Sigma$, corresponding to a finite spin density, the predictive power of the model is challenged by an ambiguity associated with a contribution of the vacuum renormalization term to the free energy. Eliminating the regularization freedom through comparison with recent low-$\mu_{\Sigma}$ lattice data, we extend the phase diagram of QCD at finite spin density to regions inaccessible to lattice simulations. We show that, as the spin potential increases, the temperature of the chiral crossover transition diminishes and the chiral crossover turns into a first-order transition at a second-order critical end-point $(T,\mu_\Sigma)_\mathrm{CEP}\simeq (0.142,0.098)$ GeV. With increasing spin potential, the critical temperature touches the zero-temperature axis at $\mu_{\Sigma} = 0.310$ GeV, implying that the chiral symmetry is restored at higher potentials at any temperature.

The (degenerate) geometry of event horizons is linked to Carrollian fluids. We investigate the behavior of event horizons via a perturbative coupling to a massless scalar field, making connections to Carrollian hydrodynamics with a driving source, and discuss the fluid equilibration in tandem with the horizon's relaxation to equilibrium. We observe that after the perturbation dies off, the Carrollian fluid energy and momentum densities approach equilibrium as the horizon asymptotically becomes non-expanding. We connect the equilibration of the Carrollian fluid dual to the black hole horizon through the expansion of its background geometry.

According to the Kibble-Zurek mechanism (KZM), the density of topological defects created during a second-order phase transition is determined by the correlation length at the freeze-out time. This suggests that the final configuration of topological defects in such a transition is largely established during the impulse regime, soon after the critical point is traversed. Motivated by this, we conjecture that machine learning (ML) can predict the final configuration of topological defects based on the time evolution of the order parameter over a short interval in the vicinity of the critical point, well before the order parameter settles into the emerging new minima resulting from spontaneous symmetry breaking. Furthermore, we show that the predictability of ML also follows the power law scaling dictated by KZM. We demonstrate these using a Recurrent Neural Network.

In this work, we investigate bound periodic orbits of timelike particles in the spacetime of dyonic black holes arising from quasi-topological electromagnetic theory. By varying the coupling parameter $\alpha_1$, the corresponding black hole solutions exhibit diverse horizon structures, including naked singularities and black holes with one to four horizons. We find that for sufficiently small $\alpha_1$, the metric function $f(r)$ becomes non-monotonic outside the event horizon in spacetimes with one or two horizons, while in all other cases, $f(r)$ remains strictly monotonic. In the non-monotonic regime, the radial effective potential develops a double-barrier structure, allowing the emergence of multiple marginally bound orbits and multiple branches of periodic orbits associated with the same rational number $l$. Although differing in radial structure, these orbit branches are topologically equivalent. Remarkably, when the outer potential barrier exceeds unity, bound orbits with energy $E>1$ become possible, in addition to the standard $E<1$ branches. When the peak reaches $E=1$, up to three distinct bound orbit branches may coexist. We also identify a novel eccentricity behavior, the innermost branch becomes increasingly circular with increasing energy or angular momentum, while outer branches exhibit greater eccentricity and a larger apastron-periastron separation. These features, absent in previous studies, are unique signatures of non-monotonic metric functions. In contrast, monotonic cases yield a single-well potential, a unique marginally bound orbit, and a single periodic orbit branch per $q$, consistent with earlier findings. Our results highlight the critical role of the metric function's shape in determining the orbital structure around dyonic black holes.

It has long been known that the gluon propagator in Landau-gauge QCD exhibits a mass gap; and its emergence has been ascribed to the action of the Schwinger mechanism in the gauge sector of QCD. In the present work, we relate this property to the physical mass gap of QCD by considering two observables associated with confinement and chiral symmetry breaking, namely the confinement-deconfinement transition temperature and the pion decay constant, respectively. It turns out that the first observable is linearly proportional to the gluon mass gap, a fact that allows us to assign a direct physical meaning to this scale. Moreover, we identify three distinct momentum regimes in the gluon propagator, ultraviolet, intermediate, and deep infrared, and assess their impact on the aforementioned observables. Both observables are sensitive to the first two regions of momenta, where functional approaches essentially coincide, but are insensitive to the third, deep infrared, regime. The combined information is used for a simple fit for the gluon propagator, all of whose parameters admit a clear physical interpretation. Finally, we discuss how this fit can help us access the intertwined dynamics of confinement and chiral symmetry breaking in QCD-type theories.

Let $f_1,f_2$ be holomorphic modular forms of the same weight for a cocompact lattice $\Gamma < \mathrm{PSL}_2(\mathbf{R})$. We estimate the rate of decay of the coefficients in the expansion of $f_1\overline{f_2}$ in a Laplace eigenbasis. By specializing our main theorem to the case where $\Gamma$ is arithmetic, we obtain new instances of the Weyl bound for triple product $L$-functions in the spectral aspect. Our method builds on the conformal bootstrap in physics.

Effective String Theory (EST) offers a robust non-perturbative framework for describing confinement in Yang-Mills theory by treating the confining flux tube between a static quark-antiquark pair as a thin, vibrating string. While EST calculations are typically carried out using zeta-function regularization, certain problems-such as determining the flux tube width-are too complex to solve analytically. However, recent studies have demonstrated that EST can be explored numerically by employing deep learning techniques based on generative algorithms. In this work, we provide a brief introduction to EST and this novel numerical approach. Finally, we present results for the width of the Nambu-Gotö EST.

We present precise theoretical results for the $ZH$ production cross section and invariant mass distribution at the Large Hadron Collider (LHC) taking into account the effects of soft gluons. We improve both quark-initiated and gluon-initiated subprocesses through threshold resummation within the QCD framework and present combined results relevant for $13.6$ TeV LHC.

This work investigates a relativistic quantum Otto engine with a harmonic oscillator as its working medium, analyzing how relativistic motion and nonadiabatic driving affect its performance and efficiency bounds. In the adiabatic regime, a closed-form analytical expression is derived for the generalized Carnot efficiency, which incorporates the effects of relativistic motion and reduces to the standard Carnot efficiency in the nonrelativistic limit. For nonadiabatic driving, we consider sudden compression and expansion work strokes and show that the maximum efficiency achievable by the engine is limited to 1/2, even in the ultra-relativistic limit. Going one step further, we also derive an analytical expression for the efficiency bound in the sudden-switch protocol, which can be regarded as the nonadiabatic counterpart of the generalized Carnot efficiency. Together, these results provide analytical bounds for the efficiency of relativistic quantum heat engines and constitute the first systematic study of the interplay between relativistic motion and frictional effects arising from nonadiabatic driving.

In double charmonium production, a long-standing challenge is that the theoretical predictions are not consistent with the measurements at B factories. Within the NRQCD framework, the next-to-leading order (NLO) calculation has proved its power to cut down the discrepancy between theory and experiments. To further clarify this puzzle, we have performed the next-to-next-to-leading order (NNLO) calculation. The amplitude is obtained as an analytical asymptotic expansion in the ratio of the squared charm-quark mass over the squared center-of-mass energy, $m_c^2/s$. We investigate the origin of the leading logarithms by performing a region analysis, revealing the intricate factorization structure in this process. We provide numerical predictions on the total cross sections of $J/\psi+\eta_c$ production, which agree with the experimental results. Extension of our computation to $\Upsilon+\eta_b$ production is also discussed.

The singularities present at the centre of black holes signal a break down of the classical theory. In this paper, we demonstrate a resolution of the Schwarzschild-(Anti-)de Sitter singularity by imposing unitary evolution with respect to unimodular time. Employing the Henneaux-Teitelboim formulation of unimodular gravity, we perform a canonical quantization on a symmetry-reduced Schwarzschild-(Anti-) de Sitter model. This leads to a Wheeler-DeWitt equation that effectively becomes a Schrödinger equation in unimodular time. By imposing unitarity, we discover a family of quantum theories in which the classical singularity is resolved. These theories each allow only semiclassical states corresponding to one mass sign: either positive, negative, or zero. Furthermore, we derive an analytical expression for the quantum-corrected Schwarzschild metric, which is modified by a new length scale $r_{min}$ that governs the black hole's transition to a white hole.

We examine the dynamics of the three-state Potts quantum spin chain in the extreme ferromagnetic regime using perturbation theory in the transverse magnetic field. We demonstrate that this approach provides access to features well beyond the semiclassical method applied previously, including the description of resonant excitations and analytic prediction for the time evolution after a quantum quench. We also demonstrate that it agrees with the meson/bubble spectrum results from exact diagonalisation and the numerical simulations of the time evolution.

A fermion can be chiral or vectorlike with respect to a given symmetry, depending on its coupling to the corresponding gauge boson. Vectorlike fermions have a distinct property that their left-handed and right-handed components behave in the same way under the gauge symmetry. In this paper, we investigate an extension of the standard model with an $SU(2)$ doublet of vectorlike leptons and two complex scalars. The new physics effects on the lepton anomalous magnetic moment, as well as the electron and muon pair production processes at $e^+e^-$ colliders are analyzed. Taking into account the updated measurement results of the electron and muon $g-2$, the LEP and the LHC data, the viable parameter space of the model is identified. We also examine the prospect of testing the model using $\mu^+\mu^-$ signals from electron-position annihilation at the Future Circular Collider (FCC-ee). The analysis shows that the FCC-ee will be able to exclude a significant part of the parameter space, pinpointing exiguous viable regions to be tested in the future due to its high precision.

While tremendous research has revealed that symmetry enriches topological phases of matter, more general principles that protect topological phases have yet to be explored. In this Letter, we elucidate the roles of subspaces in free-fermionic topological phases. A subspace property for Hamiltonians enables us to define new topological invariants. They result in peculiar topological boundary phenomena, i.e., the emergence of an unpaired zero mode or zero-winding skin modes, characterizing subspace-protected topological phases. We establish and demonstrate the bulk-boundary correspondence in subspace-protected topological phases. We further discuss the interplay of the subspace property and internal symmetries. Toward application, we also propose possible platforms possessing the subspace property.

Recent observations of the cosmic microwave background (CMB) and baryon acoustic oscillations (BAO) show some tension with a $\Lambda$CDM cosmology. For one, the cosmological parameters determined by the CMB are at odds with the expansion history determined by latest BAO measurements. In addition, the combined data has placed uncomfortably strong constraints on neutrino mass. Both effects can be interpreted as negative neutrino mass, one describing the change to the expansion history and the other one describing enhanced lensing. In this paper, we show the current tensions can be solved with a single change either to the lensing of the CMB or the expansion of the universe. We show additional lensing could arise from a variety of models with new light fields. However, these models rarely give the same signal in temperature and polarization, giving a concrete test of the scenario. Alternatively, dark sector models can explain the changes to the expansion by changing the evolution of the matter density. These models introduce new forces, giving rise to long range signals in the three-point statistics of galaxies. We discuss a range of other examples which all illustrate the pattern that additional signals should appear if these tensions are explained by beyond the Standard Model physics.

The auxiliary field sigma model (AFSM) has recently been constructed by Ferko and Smith as deformations of the principal chiral model by including auxiliary fields and the potential term given by an arbitrary univariate function. This AFSM provides an infinite family of integrable sigma models including the original $T\overline{T}$-deformation and the root $T\overline{T}$-deformation. In this paper, we propose a 4D Chern-Simons (CS) theory with auxiliary fields. Then the AFSM is derived from this CS theory with the twist function for the principal chiral model by imposing appropriate boundary conditions for the gauge field and auxiliary fields. We also derive the AFSM with the Wess-Zumino term by deforming the twist function and modifying the boundary conditions.

The physics of strongly correlated systems offers some of the most intriguing physics challenges such as competing orders or the emergence of dynamical composite degrees of freedom. Often, the resolution of these physics challenges is computationally hard, but can be simplified enormously by a formulation in terms of the dynamical degrees of freedom and within an expansion about the physical ground state. Importantly, such a formulation does not only reduce or minimise the computational challenges, it also facilitates the access to the physics mechanisms at play. The tasks of finding the dynamical degrees of freedom and the physical ground state can be systematically addressed within the functional renormalisation group approach with flowing fields which accommodates both, emergent composites as well as the physical ground state. In the present work we use this approach to set up physics-informed renormalisation group flows (PIRG flows): Scale-dependent coordinate transformations in field space induce emergent composites, and the respective flows for the effective action generate a large set of target actions, formulated in these emergent composite fields. This novel perspective on RG flows bears a great potential both for conceptual as well as computational applications: to begin with, PIRG flows allow for a systematic search of the dynamical degrees of freedom and the respective ground state that leads to the most rapid convergence of expansion schemes, thus minimising the computational effort. Secondly, the resolution of the remaining computational tasks within a given expansion scheme can be further reduced by optimising the physics content within a given approximation. Thirdly, the maximal variability of PIRG flows can be used to reduce the analytic and numerical effort of solving the flows within a given approximation.

In these lecture notes for the Les Houches School on Quantum Geometry I give an introductory overview of non-perturbative aspects of topological string theory. After a short summary of the perturbative aspects, I first consider the non-perturbative sectors of the theory as unveiled by the theory of resurgence. I give a self-contained derivation of recent results on non-perturbative amplitudes, and I explain the conjecture relating the resurgent structure of the topological string to BPS invariants. In the second part of the lectures I introduce the topological string/spectral theory (TS/ST) correspondence, which provides a non-perturbative definition of topological string theory on toric Calabi-Yau manifolds in terms of the spectral theory of quantum mirror curves

We explore the correspondence between the parallel surfaces framework, and the minimal surfaces framework, to uncover and apply new aspects of the geometrical and mechanical content behind the so-called Lovelock-type brane gravity (LBG). We show how this type of brane gravity emerges naturally from a Dirac-Nambu-Goto (DNG) action functional built up from the volume element associated with a world volume shifted a distance $\alpha$ along the normal vector of a germinal world volume, and provide all known geometric structures for such a theory. Our development highlights the dependence of the geometry for the displaced world volume on the fundamental forms, as well as on certain conserved tensors, defined on the outset world volume. Based on this, LBG represents a natural and elegant generalization of the DNG theory to higher dimensions. Moreover, our development allows for exploring disformal transformations in Lovelock brane gravity and analyzing their relations with scalar-tensor theories defined on the brane trajectory. Likewise, this geometrical correspondence would enable us to establish contact with tractable Hamiltonian approximations for this brane gravity theory, by exploiting the linkage with a DNG model, and thus start building a suitable quantum version.

Boundaries in gauge theory and gravity give rise to symmetries and charges at both finite and asymptotic distance. Due to their structural similarities, it is often held that soft modes are some kind of asymptotic limit of edge modes. Here, we show in Maxwell theory that there is an arguably more interesting relationship between the asymptotic symmetries and their charges, on one hand, and their finite-distance counterparts, on the other, without the need of a limit. Key to this observation is to embed the finite region in the global spacetime and identify edge modes as dynamical $\rm{U}(1)$-reference frames for dressing subregion variables. Distinguishing intrinsic and extrinsic frames, according to whether they are built from field content in- or outside the region, we find that non-trivial corner symmetries arise only for extrinsic frames. Further, the asymptotic-to-finite relation requires asymptotically charged ones (like Wilson lines). Such frames, called soft edges, extend to asymptotia and, in fact, realize the corner charge algebra in multiple ways, for example, by "pulling in" the asymptotic one from infinity, or physically through the addition of asymptotic soft and hard radiation. Realizing an infinite-dimensional algebra requires a new set of soft boundary conditions, relying on the distinction between extrinsic and intrinsic data. We identify the subregion Goldstone mode as the relational observable between extrinsic and intrinsic frames and clarify the meaning of vacuum degeneracy. We also connect the asymptotic memory effect with a more operational quasi-local one. A main conclusion is that the relationship between asymptotia and finite distance is frame-dependent; each choice of soft edge mode probes distinct cross-boundary data of the global theory.

We propose a Lorentz covariant matrix model as a nonperturbative formulation of the bosonic M2-brane in M-theory. Unlike previous approaches relying on the light-cone gauge or symmetry-based constructions, our model retains full 11-dimensional Lorentz invariance by introducing a novel gauge-fixing condition that restricts the symmetry of volume-preserving deformations (VPD) to a subclass, which we call restricted VPD (RVPD). This restriction enables a consistent matrix regularization of the Nambu bracket, bypassing the long-standing obstructions related to the Leibniz rule and the Fundamental Identity. The resulting model exhibits RVPD symmetry, admits particle-like and noncommutative membrane solutions, and lays the foundation for a Lorentz-invariant, nonperturbative matrix description of M2-branes. Our work offers a new paradigm for constructing Lorentz-invariant matrix models of membranes, revisiting the algebraic structure underlying M-theory.

In this paper, we develop and explore recursive methods to investigate the 2d CFT 5-point conformal block with a level 2 degenerate insertion, as well as its AGT dual, by solving the BPZ differential equation. First, we represent the solution of the differential equation as a double series expansion. On the 2-node quiver gauge theory side, this corresponds to the instanton series. We then demonstrate that the expansion coefficients are uniquely determined by a recursion relation. Inspired by the approach initiated in a paper by D. Gaiotto and J. Teschner, we partially resum this series and show that the result can be elegantly expressed in terms of a single hypergeometric function and its derivative. This new representation makes it straightforward to relate different asymptotic regions. As a by-product, this provides us a simple derivation of fusion and braiding coefficients. We describe the subtle procedure of merging the degenerate field with the outgoing state, thereby obtaining a generic 4-point block, which on the gauge theory side corresponds to the partition function of $SU(2)$ gauge theory with four massive hypermultiplets in the $\Omega$-background. Finally, we performed several nontrivial checks that confirm our results.

We study classical wormhole solutions in 3D gravity with end-of-the-world (EOW) branes, conical defects, kinks, and punctures. These solutions compute statistical averages of an ensemble of boundary conformal field theories (BCFTs) related to universal asymptotics of OPE data extracted from the 2D conformal bootstrap. Conical defects connect BCFT bulk operators; branes join BCFT boundary intervals with identical boundary conditions; kinks (1D defects along branes) link BCFT boundary operators; and punctures (0D defects) are endpoints where conical defects terminate on branes. We provide evidence for a correspondence between the gravity theory and the ensemble. In particular, the agreement of the $g$-function dependence results from an underlying topological aspect of the on-shell EOW brane action, from which a BCFT analogue of the Schlenker-Witten theorem also follows.

Instead of the much more involved covariant counterterm method, we apply the well justified background subtraction method to calculate the first order corrections to Kerr-AdS black hole thermodynamics induced by the higher derivative terms up to the cubic of Riemann tensor, where the computation is further simplified by the decomposition trick for the bulk action. The validity of our results is further substantiated by examining the corrections induced by the Gauss-Bonnet term. Moreover, by comparing our results with those obtained via the ADM and Wald formulas in Lorentzian signature, we can extract some generic information about the first order corrected black hole solution induced by each higher derivative term.

We study a Hermitian matrix model with a quartic potential, modified by a curvature term $\mathrm{tr}(R\Phi^2)$, where $R$ is a fixed external matrix. Inspired by the truncated Heisenberg algebra formulation of the Grosse--Wulkenhaar model, this term breaks unitary invariance and, through perturbative expansion, induces an effective multitrace matrix model. We analyze the resulting action both analytically and numerically, including Hamiltonian Monte Carlo simulations, focusing on the shift of the triple point and suppression of the noncommutative striped phase -- two features closely tied to renormalizability. Our findings show that the curvature term drives the phase structure toward renormalizable behavior by removing the striped phase in the large-$N$ limit, while also unexpectedly revealing a novel multi-cut phase deep in the perturbative regime, at least for fixed matrix size.

We derive a universal formula for the overlaps between integrable matrix product states (MPS) and Bethe eigenstates in $\mathfrak{gl}_{N}$ symmetric spin chains. This formula expresses the normalized overlap as a product of a MPS-independent Gaudin-determinant ratio and a MPS-dependent scalar factor constructed from eigenvalues of commuting operators, defined via the $K$-matrix associated with the MPS. Our proof is fully representation-independent and relies solely on algebraic Bethe Ansatz techniques and the $KT$-relation. We also propose a generalization of the overlap formula to $\mathfrak{so}_{N}$ and $\mathfrak{sp}_{N}$ spin chains, supported by algebra embeddings and low-rank isomorphisms. These results significantly broaden the class of integrable initial states for which exact overlap formulas are available, with implications for quantum quenches and defect CFTs.

Six dimensional $\mathcal{N}=(1,0)$ supergravity features BPS strings whose properties encode highly nontrivial information about the parent 6d theory. We focus on a distinguished set of theories whose string charge lattice is one-dimensional. In geometric theories, the generator of the lattice arises from a D3 brane wrapping the hyperplane class in $\mathbb{P}^2$. This hyperplane string is expected to remain stable even when one ventures beyond the geometric regime where it becomes challenging to verify which candidate 6d theories belong to the swampland. We identify five 6d models which from the perspective of the hyperplane string deviate the most from being geometric. For these theories we are able to provide an exact description of the left-moving sector of the hyperplane string worldsheet in terms of a rational conformal field theory and provide evidence for their consistency. In one instance, using RCFT methods we are able to determine the elliptic genus and find that in the unflavored limit it matches with the elliptic genus of geometric models. We argue that the non-geometric model is connected to geometric ones via a sequence of Higgsing transitions. These results lead us to formulate a proposal relating the quantum corrected moduli space of the hyperplane string CFT with a region of the landscape of 6d $(1,0)$ quantum gravity.

We identify new families of duality-invariant theories of electrodynamics. We achieve this in two different ways. On the one hand, we present an algorithm to construct a one-parameter family of exactly duality-invariant theories from a single seed duality-invariant theory. If the seed theory is causal, the theories constructed from this method will also be causal when the parameter is non-negative. On the other hand, we find two additional novel families of duality-invariant theories which include a nonzero term independent of the electromagnetic field. The first of them generalizes Bialynicki-Birula electrodynamics, while the second family of theories features a well-defined Maxwell limit as the term independent of the gauge field strength is sent to zero.

We explore asymptotically locally anti-de Sitter spacetimes exhibiting gravitational radiative behavior, employing null gauges that allow for a well-defined flat limit. The radiative content in the bulk is captured by the boundary Cotton and stress tensor, which we collect into a radiative vector. We reinterpret this vector holographically in terms of fluid variables in the dual boundary theory. For algebraically special solutions, we uncover a close connection between bulk radiation and dissipative corrections in the boundary stress tensor, demonstrating a direct link between radiation and entropy production in the boundary fluid. This reveals a rich interplay between radiative dynamics in the bulk and out-of-equilibrium conformal physics at the boundary. We then investigate the flat limit of this correspondence in the context of flat-space holography. In this setting, we construct a Carrollian analogue of the radiative vector and introduce Celestial observables, such as energy detectors, which emerge naturally from the bulk's radiative structure. Our analysis shows that bulk radiation sources the Carrollian viscous stress tensor and heat current, which encodes the Bondi news in this framework. We illustrate our results with explicit examples, including Robinson-Trautman spacetimes and accelerating black holes.

It has been shown that the non-Abelian vortex string in 4D $\mathcal{N}=2$ SQCD with the U(2) gauge group and $N_f=4$ flavors becomes a critical superstring. Its 10D target space is a product of the flat 4D space and an internal noncompact Calabi-Yau threefold, namely, the conifold. It was also shown that the Coulomb branch of the associated string sigma model, which opens up at strong coupling, can be described by $\mathcal{N}=2$ Liouville theory. We continue here the study of the recently proposed mass deformation of the U(2) theory with $N_f=4$, interpolating to SQCD with the U(4) gauge group and $N_f=8$ quarks, by analyzing the mass-deformed $\mathcal{N}=2$ Liouville theory on the string world sheet, and show that it is always described by the trumpet geometry of the target space, which is $T$-dual to the 2D $\mathcal{N}=2$ supersymmetric black hole. We use this correspondence to find the low-lying hadron spectrum in the deformed SQCD, and explain the expected increase in the number of hadronic states in the theory with more gauge fields and quarks by considering the near-Hagedorn behavior of the 2D black hole.

We calculate the chiral effective superpotential in $4D$ $\mathcal{N}=1$, $SU(N)$ super Yang-Mills theory coupled to chiral matter in one- and two-loop approximations. It is found that the one-loop contribution to the chiral effective potential is always finite and is expressed in terms of a specific triangle integral. The two-loop contributions generated by purely chiral vertices turned out to be finite as well. The chiral effective potential stipulated by supergraphs with gauge superfield subgraphs is finite for the supergraphs with no divergent subgraphs. In the case of the finite $\mathcal{N}=2$ SYM theory, the two-loop chiral contributions to the effective action are significanlty simplified. The leading large $N$ behavior of the chiral effective superpotential in finite $\mathcal{N}=2$ super-Yang-Mills models with $SU(N)$ gauge symmetry is studied and it is shown that the exact form in the coupling constant of the chiral effective superpotential can be found.

A large primordial lepton asymmetry can lead to successful baryogenesis by preventing the restoration of electroweak symmetry at high temperatures, thereby suppressing the sphaleron rate. This asymmetry can also lead to a first-order cosmic QCD transition, accompanied by detectable gravitational wave (GW) signals. By employing next-to-leading order dimensional reduction we determine that the necessary lepton asymmetry is approximately one order of magnitude smaller than previously estimated. Incorporating an updated QCD equation of state that harmonizes lattice and functional QCD outcomes, we pinpoint the range of lepton flavor asymmetries capable of inducing a first-order cosmic QCD transition. To maintain consistency with observational constraints from the Cosmic Microwave Background and Big Bang Nucleosynthesis, achieving the correct baryon asymmetry requires entropy dilution by approximately a factor of ten. However, the first-order QCD transition itself can occur independently of entropy dilution. We propose that the sphaleron freeze-in mechanism can be investigated through forthcoming GW experiments such as $\mu$Ares.

We show that the existence of massive neutron stars and asymptotic freedom of QCD place robust upper bounds on the lowest sound speed of the ultra-dense matter unattainable in neutron stars. Centered on worst-case scenarios, our limits are the most conservative among physical equations of state in the density range $\sim 2-40 n_0$. Discovery of $\gtrsim 2.6 M_\odot$ neutron stars, in combination with current multimessenger astrophysical constraints on the equation of state, would strongly support first-order phase transitions at high baryon densities.

In the last decade, the first law of binary black hole mechanics played an important unifying role in the gravitational two-body problem. More recently, binary black hole scattering and the application of high-energy physics methods have provided a new avenue into this classical problem. In this Letter, we connect these two themes by extending the first law to the case of scattering orbits. We present derivations based on classical S-matrix, Hamiltonian, and pseudo-Hamiltonian methods, the last of which allows us to include dissipative effects for the first time. Finally, a "boundary to bound" map links this first law to the traditional bound-orbit version. Through this map a little-known observable for scatter orbits, the elapsed proper time, is mapped to the Detweiler redshift for bound orbits, which is an invariant building block in gravitational waveform models.

I carry out numerical scattering calculations against a family of finite-length one-dimensional point-like arrangements of atoms, $\chi(x)$, related to the distribution of prime numbers by a shift operation making the atomic density approximately constant. I show how the Riemann Zeta Function (RZF) naturally parameterizes the analytic structure of the scattering amplitude and give numerical results.

The nature of one-loop corrections to long-wavelength CMB-scale modes in single-field inflation models with an intermediate USR phase remains a subject of active debate. In this work, we perform a detailed investigation into the regularization and renormalization of these one-loop corrections to the curvature perturbation power spectrum. Employing a combined UV-IR regularization scheme within the in-in formalism, we compute the regularized one-loop contributions, including those from the tadpole diagram, arising from both the cubic and quartic interaction Hamiltonians. We demonstrate that the fully regularized and renormalized fractional loop correction to the power spectrum is controlled by its peak value at the end of the USR phase, scaling as $\mathcal{P}_\mathrm{peak} \sim e^{6 \Delta N}$, where $\Delta N$ is the duration of the USR phase. This result confirms the original conclusion that loop corrections can become non-perturbatively large if the transition from the USR phase to the final slow-roll phase is instantaneous and sharp, potentially challenging the validity of such inflationary scenarios for primordial black hole formation.

We present the first constraints on primordial magnetic fields from the Lyman-$\alpha$ forest using full cosmological hydrodynamic simulations. At the scales and redshifts probed by the data, the flux power spectrum is extremely sensitive to the extra power induced by primordial magnetic fields in the linear matter power spectrum, at a scale that we parametrize with $k_{\rm peak}$. We rely on a set of more than a quarter million flux models obtained by varying thermal, reionization histories and cosmological parameters. We find a hint of extra power that is well fitted by the PMF model with $B\sim 0.2$ nG, corresponding to $k_{\rm peak}\sim 20$ Mpc$^{-1}$. However, when applying very conservative assumptions on the modelling of the noise, we obtain a 3$\sigma$ C.L. lower limit $k_{\rm peak}> 30$ Mpc$^{-1}$ which translates into the tightest bounds on the strength of primordial intergalactic magnetic fields: $B < 0.30$ nG (for fixed, nearly scale-invariant $n_{\rm B}=-2.9$).

We study the dynamics of entanglement asymmetry in random unitary circuits (RUCs). Focusing on a local $U(1)$ charge, we consider symmetric initial states evolved by both local one-dimensional circuits and geometrically non-local RUCs made of two-qudit gates. We compute the entanglement asymmetry of subsystems of arbitrary size, analyzing the relaxation time scales. We show that the entanglement asymmetry of the whole system approaches its stationary value in a time independent of the system size for both local and non-local circuits. For subsystems, we find qualitative differences depending on their size. When the subsystem is larger than half of the full system, the equilibration time scales are again independent of the system size for both local and non-local circuits and the entanglement asymmetry grows monotonically in time. Conversely, when the subsystems are smaller than half of the full system, we show that the entanglement asymmetry is non-monotonic in time and that it equilibrates in a time proportional to the quantum-information scrambling time, providing a physical intuition. As a consequence, the subsystem-equilibration time depends on the locality of interactions, scaling linearly and logarithmically in the system size, respectively, for local and non-local RUCs. Our work confirms the entanglement asymmetry as a versatile and computable probe of symmetry in many-body physics and yields a phenomenological overview of entanglement-asymmetry evolution in typical non-integrable dynamics.

As quantum analogs of the classical Kolmogorov-Sinai entropy, quantum dynamical entropies have emerged as important tools to characterize complex quantum dynamics. In particular, Alicki-Fannes-Lindblad (AFL) entropy, which quantifies the information production of a coherent quantum system subjected to repeated measurement, has received considerable attention as a potential diagnostic for quantum chaos. Despite this interest, the precise behavior of quantum dynamical entropy in the presence of symmetry has seen little study. In this work, we establish rigorous inequalities of the AFL entropy for arbitrary unitary dynamics (single-particle and many-body) in the presence of various types of symmetry. Our theorems encompass three cases: Abelian symmetry, an anticommuting unitary, and non-Abelian symmetries. We motivate our main results with numerical simulations of the perturbed quantum cat maps. Our findings highlight the role of symmetry in quantum dynamics under measurements, and our framework is easily adaptable for study of symmetry in other probes of quantum chaos.

Numerical studies of phase transitions in statistical and quantum lattice models provide crucial insights into the corresponding Conformal Field Theories (CFTs). In higher dimensions, comparing finite-volume numerical results to infinite-volume CFT data is facilitated by choosing the sphere $S^{d-1}$ as the spatial manifold. Recently, the fuzzy sphere regulator in Ref. [Zhu et al, Phys. Rev. X 13 021009 (2023)] has enabled such studies with exact rotational invariance, yielding impressive agreement with known 3D Ising CFT predictions, as well as new results. However, systematic improvements and a deeper understanding of finite-size corrections remain essential. In this work, we revisit the fuzzy sphere regulator, focusing on the original Ising model, with two main goals. First, we assess the robustness of this approach using Conformal Perturbation Theory (CPT), to which we provide a detailed guidebook. We demonstrate how CPT provides a unified framework for determining the critical point, the speed of light, and residual deviations from CFT predictions. Applying this framework, we study finite-size corrections and clarify the role of tuning the model in minimizing these effects. Second, we develop a novel method for extracting Operator Product Expansion (OPE) coefficients from fuzzy sphere data. This method leverages the sensitivity of energy levels to detuning from criticality, providing new insights into level mixing and avoided crossings in finite systems. Our work also includes validation of CPT in a 1+1D Ising model away from the integrable limit.

We perform the shadow radius analysis of a charged Horndeski black hole (CHB) and the naked singularity (NS) with secondary scalar hair obtained from the Einstein-Horndeski-Maxwell theory. For this analysis, we include the beyond Horndeski black hole (bH) with secondary scalar hair and the magnetically charged black hole (MC) found from the Einstein-Euler-Heisenberg theory. It is worth noting that the NS versions of CHB and bH arise from the charge extension of their photon spheres, while there is no NS version for MC. One branch (i) from the CHB is a point in the horizon realization but it shows up on the photon sphere and shadow radius. The shadow radius for the CHB is the nearly same as that for the MC with a single horizon and the charge of the NS is constrained by the EHT observation. From classical scattering analysis, it turns out that i-NS and NS play different roles from CHB, bH, and MC.

This study sets new constraints on Cold+Warm Dark Matter (CWDM) models by leveraging the small-scale suppression of structure formation imprinted in the Lyman-$\alpha$ forest. Using the Sherwood-Relics suite, we extract high-fidelity flux power spectra from simulated Lyman-$\alpha$ forest data, spanning a broad range of cosmologies and thermal histories. This enables precise constraints on the warm dark matter (WDM) fraction, $f_{\mathrm{WDM}}$, and the mass of the WDM particle, $m_{\mathrm{WDM}}$. A key advancement of our analysis is the integration of a neural network emulator directly at the likelihood level, significantly accelerating Bayesian parameter inference. With new observations of high-redshift ($z$ = 4.2$-$5.0) quasar spectra from UVES and HIRES, we establish stringent upper limits: for $m_{\mathrm{WDM}}$ = 1 keV, we find $f_{\mathrm{WDM}} < 0.16$ (2$\sigma$), with constraints loosening to 35\%, 50\%, and 67\% for $m_{\mathrm{WDM}}$ = 2, 3, and 4 keV, respectively. Our results for pure WDM reaffirm the lower bounds of previous work. Crucially, we account for the fixed resolution of simulations and the impact of patchy reionization, demonstrating their minimal influence on mixed dark matter constraints. This robustness paves the way for tighter bounds with improved statistical samples in the future. Our findings suggest that CWDM models can naturally accommodate mild suppression of matter clustering in the high redshift Lyman-$\alpha$ forest 1D flux power, potentially offering a resolution to some of the ongoing cosmological tensions at low redshifts, namely the $S_{8}$ tension.

Heavy-ion collision experiments such as the Large Hadron Collider and the Relativistic Heavy Ion Collider offer a unique platform to study several key properties of the quark-gluon plasma (QGP), a deconfined state of strongly interacting matter. Quarks, being the electrically charged particles, can induce an electric current in the medium in response to the temperature gradients. Hence, the QGP medium can behave like a thermoelectric medium. The thermoelectric coefficients, such as the Seebeck and Thomson coefficients, can help us to understand the intricate transport phenomenon of the medium. In peripheral collisions, the intense, transient, and time-dependent magnetic field created due to spectator protons significantly influences the thermoelectric properties of the QGP medium, affecting the charge and heat transport. This work uses the quasi-particle model to calculate the Thomson coefficient in QGP. The Thomson effect, describing the continuous heating or cooling of the charge-carrying medium in the presence of temperature gradients, remains largely unexplored in QGP. The Seebeck effect, which relates temperature gradients to induced electric fields, has been widely studied in the literature. For the first time, we calculate the magneto-Thomson and transverse Thomson coefficients. We have studied their dependence on temperature, baryon chemical potential, center of mass energy, and time-dependent magnetic field with different decay parameters. The transverse Thomson effect originates due to the presence of the Nernst effect in the presence of a magnetic field. Our results provide new insights into the higher-order thermoelectric transport properties of the QGP medium in the context of heavy-ion collisions.

The Polyakov Quark Meson (PQM) model is extended to SU(4) flavor symmetry by incorporating the charm quark and introducing a finite isospin asymmetry. This model incorporates the light, strange, and charm chiral condensates, along with the Polyakov-loop variables, to describe the confinement--deconfinement phase transition in a thermal and dense QCD medium. The inclusion of the charm quark condensate enhances the capability of the SU(4) PQM model to explore the spatial and thermal resolution of the chiral phase structure, particularly in the crossover and high-temperature regimes. We construct the QCD phase diagram ($T/T_\chi-\mu_I/m_\pi$) plane, indicating a decrease in the pseudo-critical temperature as the isospin chemical potential increases and explore thermodynamic quantities related to the QCD equation of state at very high temperatures. Fluctuations of quark flavors, conserved charges and baryon-charm correlations are studied across a wide temperature range. The SU(4) PQM model exhibits good qualitative agreement with lattice QCD calculations. Additionally, we calculate the meson mass spectrum at zero and finite temperature, showing that the charm sector remains thermally stable over a wide temperature range. Overall, this study highlights the capability of the SU(4) PQM model to describe key features of QCD matter at high temperatures and its relevance to heavy-ion collisions and astrophysical studies.

We study the class of six-dimensional $\Lambda$-vacuum spacetimes which admit a non-degenerate multiple Weyl aligned null direction l (thus being of Weyl type~II or more special) with a ``generic'' optical matrix. Subject to an additional assumption on the asymptotic fall-off of the Weyl tensor, we obtain the most general metric of this class, which is specified by one discrete (normalized) and three continuous parameters. All solutions turn out to be Kerr--Schild spacetimes of type~D and, in passing, we comment on their Kerr--Schild double copy. We further show that the obtained family is locally isometric to the general doubly-spinning Kerr-NUT-(A)dS metric with the NUTs parameters switched off. In particular, the Kerr-(A)dS subclass and its extensions (i.e., analytic continuation and ``infinite-rotation'' limit) are recovered when certain polynomial metric functions are assumed to be fully factorized. As a side result, a unified metric form which encompasses all three branches of the extended Kerr-(A)dS family in all even dimensions is presented in an appendix.

We model a single black hole in equilibrium with a dark photon-cold dark matter environment. Representing the dark photon as a Proca field, we show that a Schwarzschild black hole grows vector-field "hair" when allowed to accrete from an infinite homogeneous bath of particles far from the horizon. We solve the Proca equation in linear perturbation theory, separating it using the vector spherical harmonics and Frolov-Krtouš-Kubizňák-Santos approaches for the odd-parity and even-parity sectors, respectively. In the "particle" dark matter regime, the field is purely infalling and exhibits a sharply peaked density profile, in concordance with the particle dark matter "spikes" studied in the literature. In the "wave" regime, the field exhibits standing waves, and the profile is smeared. We find a dark-matter density amplification upward of $10^7$ near the horizon. Though small for most black holes, we find the mass enclosed in the cloud can reach $\sim 1 \%$ of the black hole mass for large supermassive black holes. These black holes are also most susceptible to vector dark matter accretion, with mass accretion rates as large as $10 M_\odot/$yr.

We present an updated study of the Collins azimuthal asymmetries for pion-in-jet production in polarized $pp$ collisions. To this aim, we employ a recent extraction of the transversity and Collins fragmentation functions from semi-inclusive deep inelastic scattering and $e^+ e^-$ annihilation into hadron pairs processes, obtained within a simplified transverse momentum dependent (TMD) approach at leading order and adopting a collinear configuration for the initial state. Our theoretical estimates, when compared against 200~GeV and 510~GeV data from the STAR Collaboration, show a generally good agreement for the distributions in the transverse momentum of the jet, the pion longitudinal momentum fraction and its transverse momentum with respect to the jet direction. This corroborates the hypothesis of the universality of the Collins function as well as of the TMD factorization for such processes and, once again, of a reduced impact of the proper TMD evolution on azimuthal asymmetries. We will also present predictions based on an extraction of the Collins and transversity distributions where information from data on single spin asymmetry for inclusive pion production in $p^\uparrow p$ collisions is included through a Bayesian reweighting procedure.

This work presents a new black hole solution within the framework of a non-commutative gauge theory applied to Kalb-Ramond gravity. Using the method recently proposed in the literature [Nucl.Phys.B 1017 (2025) 116950], we employ the Moyal twist $\partial_r \wedge \partial_\theta$ to implement non-commutativity, being encoded by parameter $\Theta$. We begin by verifying that the resulting black hole no longer possesses spherical symmetry, while the event horizon remains unaffected by non-commutative corrections. The Kretschmann scalar is computed to assess the corresponding regularity. It turns out that the solution is regular, provided that the Christoffel symbols and related quantities are not expanded to second order in $\Theta$. We derive the thermodynamic quantities, including the Hawking temperature $T^{(\Theta,\ell)}$, entropy $S^{(\Theta,\ell)}$, and heat capacity $C_V^{(\Theta,\ell)}$. The remnant mass $M_{\text{rem}}$ is estimated by imposing $T^{(\Theta,\ell)} \to 0$, although the absence of a physical remnant indicates complete evaporation. Quantum radiation for bosons and fermions is analyzed via the tunneling method, where divergent integrals are treated using the residue theorem. Notably, in the low-frequency regime, the particle number density for bosons surpasses that of fermions (at least within the scope of the methods considered here). The effective potential for a massless scalar field is obtained perturbatively, enabling the computation of quasinormal modes and the time-domain profiles. Finally, further bounds on $\Theta$ and $\ell$ (Lorentz-violating paramter) are derived from solar system tests, including the perihelion precession of Mercury, light deflection, and the Shapiro time delay.

The concept of unitary randomness underpins the modern theory of quantum chaos and fundamental tasks in quantum information. In one research direction, out-of-time-ordered correlators (OTOCs) have recently been shown to probe freeness between Heisenberg operators, the non-commutative generalization of statistical independence. In a distinct setting, approximate unitary designs look random according to small moments and for forward-in-time protocols. Bridging these two concepts, we study the emergence of freeness in a random matrix product unitary (RMPU) ensemble, an efficient unitary design. We prove that, with only polynomial bond dimension, these unitaries reproduce Haar values of higher-order OTOCs for local, finite-trace observables -- precisely those predicted to thermalize in chaotic many-body systems according to the eigenstate thermalization hypothesis. We further compute the frame potential of the RMPU ensemble, showing convergence to the Haar value also with only polynomial deviations, indicating that freeness is reached on-average for global observables. On the other hand, to reproduce freeness for traceless observables, volume-law operator entanglement is required. Our results highlight the need to refine previous notions of unitary design in the context of operator dynamics, guiding us towards protocols for quantum advantage while shedding light on the emergent complexity of chaotic many-body systems.

We present a theoretical investigation of black hole solutions in Kalb-Ramond gravity embedded with quintessence fields. Our study examines how combined effects of Lorentz violation through the Kalb-Ramond field parameter $\eta$ and exotic matter contributions via quintessence parameters $(\mathrm{C}, w)$ systematically modify spacetime geometry, particle dynamics, and observational signatures compared to standard Schwarzschild black holes. The analysis encompasses geodesic motion for both photons and massive particles, revealing substantial modifications to effective potentials, photon sphere characteristics, and innermost stable circular orbit properties. We derive analytical expressions for black hole shadow radii across different quintessence states, demonstrating systematic parameter dependencies enabling observational discrimination between theoretical frameworks. Our perturbation analysis of scalar and electromagnetic fields shows how Lorentz violation and quintessence effects alter wave propagation and stability properties. Using Gauss-Bonnet theorem methodology, we calculate gravitational lensing deflection angles incorporating both modified gravity and exotic matter contributions. The thermodynamic investigation reveals complex phase structures with modified Hawking temperature evolution, Gibbs free energy characteristics, and specific heat capacity behavior significantly deviating from general relativity predictions. Lorentz violation amplifies gravitational effects, whereas quintessence exerts counteractive forces, generating complex parameter spaces allowing precise manipulation of observable quantiti

We recast the finite-region analysis of Einstein's equations that underpins the ER=EPR program into the loop quantum gravity (LQG) framework. By translating curvature-energy uncertainty relations into holonomy-flux kinematics, and by identifying Planckian Einstein-Rosen throats with single-puncture cuts through spin networks, we obtain a precise dictionary between entanglement and quantum geometry. Within this dictionary we derive the Barbero-Immirzi parameter directly from the entanglement/area increment of a minimal bridge, and show that a boundary edge-mode construction renders the Bekenstein - Hawking entropy coefficient universal and independent of $\gamma$ under a natural complex polarization. We further establish a refinement renormalization flow for spin-foam amplitudes driven by the finite-region curvature energy bound, which suppresses bubble divergences and yields a regulator-independent continuum limit under explicit conditions. Finally, we indicate observational consequences that follow from an $N$-party generalized uncertainty relation.