Motivated by quantum gravity and the CFT Distance Conjecture, we study infinite-distance limits in four-dimensional ${\cal N}=2$ superconformal field theories with higher-dimensional conformal manifolds and their AdS duals. We focus on partial decoupling limits where a gauge sector becomes weakly coupled while an interacting sector persists. We analyse the structure of towers of states emerging in these limits. The weakly coupled sector contributes, among others, the massless higher-spin tower predicted by the CFT Distance Conjecture exhibiting polynomial degeneracy. The key novelty is the appearance of a protected BPS tower in the interacting sector, characterised by exponential degeneracy and masses at the AdS scale. This structure follows from multiplet recombination in the ${\cal N}=2$ superconformal algebra: As unprotected long multiplets hit the unitarity bound at weak coupling, they recombine into protected short multiplets. We verify this picture through an explicit one-loop computation in the simplest two-node quiver gauge theory with a two-dimensional conformal manifold.

We perform a quantum probing of colliding plane-wave space-times. In particular, we consider the Khan-Penrose and the Ferrari-Ibáñez solutions, which admit a strong and a weak singularity after the two waves collide. While we find that, like Schwarzschild, for the Khan-Penrose solution the singularity cannot be probed by quantum field theory, the Ferrari-Ibáñez singularity can be traversed. Our results culminate in a quantum Weyl conjecture: The significant geometric property to classify space-times with respect to quantum probes is given by the Coulomb part of the Weyl tensor. We then use this conjecture to sketch a possible backreaction scenario for plane waves.

We consider perturbative quantum gravity as a quantum field theory of linearized metric perturbation on an asymptotically flat spacetime with a bifurcate Killing horizon. We include the perturbative gravitational constraints into the algebra of observables restricted to the right half of the future horizon of the spacetime. We use the boundary charge, associated to the horizon Killing field, as an auxiliary "observer" degree of freedom. The observables "dressed" with the additional charge are invariant under the Killing symmetry and generate a Type-$\text{II}_{\infty}$ von Neumann factor. We compute the von Neumann entropy of the reduced density matrix of a classical-quantum coherent state constructed from the metric perturbations and the "observer wavefunction". This von Neumann entropy satisfies an analogue of the first law of thermodynamics. We further show that this entropy is related to Hollands-Wald-Zhang entropy of the (second order) perturbed dynamical black hole through the flux of perturbations through the horizon and future null infinity.

We discuss aspects of the Euclidean path integral around axion-supported de Sitter wormholes, at one-loop order. We numerically compute the phase of the path integral around these solutions, as well as for a certain "multiple wormholes" generalization, and interpret this phase in different regimes. When the geometry is well approximated by a sphere with a small handle, the wormhole admits an effective description as a sphere with two local operator insertions, whose positions fluctuate around the antipodal configuration. The antipodal configuration is an extremum of the position integral for the operators, but we show that it is an unstable one. Accordingly, the phase of the wormhole solution can be viewed as the Polchinski phase in the sphere, multiplied by an additional phase from the integral over positions of the effective local operators. Using our expressions for the one-loop determinant, we also estimate the EFT coefficients of the dual bilocal operators in odd spacetime dimensions, to one-loop order. Lastly, we also discuss "maximal flux" solutions, which have $S^{1}\times S^{D-1}$ geometry. Their Lorentzian continuations are Einstein static universes, so we call them "Einstein wormholes". In this limit, we determine the spectrum of fluctuations analytically and show that the phase of the path integral around this solution is entirely accounted for by the well-known instability of the Einstein static universe.

Fredholm integral operators that commute with the Hamiltonians of certain quantum mechanical problems with quartic potentials are introduced. The operators are expressed in terms of an Airy function, and their eigenvalues fall off exponentially fast. They may help with high-accuracy numerical analysis, and their existence leads to dual descriptions in terms of infinite one-dimensional chains with variables on nodes, and weights on nodes and links. The systems discussed include the anharmonic quartic oscillator as well as multivariable potentials and higher dimensional systems, including certain quantum field theories with nonlocal interactions.

We investigate and clarify various aspects of the effective dynamics of Maxwell-Einstein-scalar theories in the background of static, spherically symmetric and asymptotically flat extremal black holes in four space-time dimensions. This rigorously places the one-dimensional effective radial dynamics governed by the Attractor Mechanism, through the critical points of the Ferrara-Gibbons-Kallosh effective black hole potential $V_{BH}$, into the Routhian formalism, a framework which is intermediate between the Lagrange and Hamilton ones, based on a partial Legendre transform, and especially relevant in presence of cyclic variables. We elucidate and analyze the interplay of a trio of effective functionals: the aforementioned $V_{BH}$, Sen's entropy functional $\mathcal{E}$, and the relevant effective Routhian functional $\mathcal{R}$. Through their critical values at the event horizon, such functionals determine the Bekenstein-Hawking and the Wald entropy of the extremal black hole.

We show that the Serreau--Tissier (ST) replica sector can dynamically generate a Gribov--Zwanziger (GZ)--type horizon functional in Yang--Mills (YM) theories. After integrating out the replica superfields, the expansion of the determinant of the Faddeev--Popov (FP) operator in the regulator $\zeta$ produces, at linear order in $\zeta$, a nonlocal kernel with the same color and Lorentz structure as the Gribov horizon functional, thereby defining an induced Gribov scale. Depending on the replica phase selected by the dynamics, the ST sector yields either (i) a local Curci--Ferrari (CF) screening mass (replica-symmetric phase) or (ii) an induced horizon-like interaction (replica-broken phase). In the latter case, the resulting BRST-invariant local formulation leads to a tree-level gluon propagator of the refined Gribov-Zwanziger (RGZ) decoupling type, whereas in the former it reduces to the massive FP/CF form, avoiding double counting of infrared scales by construction. A superspace derivation confirms that the induced horizon term originates from the ST superdeterminant, providing a microscopic mechanism for the emergence of the Gribov scale within the replica framework.

We study the solution of the gravitational field equations in $AdSL_{4}$-gauged gravity, a gauge-theoretic extension of general relativity based on the $AdSL_{4}$ algebra. In this formulation, the antisymmetric gauge field $B^{ab}$, associated with additional $AdSL_{4}$ tensorial generators, induces space-time torsion via the relation $K^{ab}=\mu B^{ab}$, where $K^{ab}$ denotes the contorsion 1-form. The presence of torsion modifies both the spin connection and curvature, leading to an extended set of Einstein-Cartan field equations. Focusing on spatially homogeneous and isotropic cosmological backgrounds, we derive the modified Friedmann equations which explicitly incorporate the torsional contribution. The resulting acceleration equation admits de Sitter-like solutions in which cosmic acceleration originates purely from the gauge-theoretic structure of enlarged four-dimensional space-time symmetries. Within this formulation, the dynamical components of the gauge field $B^{ab}$ emerge naturally as a source of the effective cosmological constants, without the introduction of exotic matter sources. Furthermore, our analysis shows that the torsion-driven cosmological phase in $AdSL_{4}$-gauged gravity can reproduce an effective equation-of-state parameter $\omega_{B}=-1/3$, establishing a connection between space-time torsion and cosmic-string-like dynamics.

We resolve the long-standing claim that regularisation by dimensional reduction (DR) fails to preserve supersymmetry in Super Yang-Mills (SYM) theories at three loops. Earlier results reported a mismatch between the Yukawa and ghost-gluon $\beta$ functions in $\mathcal{N}=2$ SYM, suggesting a breakdown of supersymmertry. We show that this discrepancy does not originate from DR itself but from subtleties in the treatment of the Clifford algebra. A corrected three-loop calculation restores full supersymmetric behaviour, and we demonstrate that the same issue would first affect $\mathcal{N}=4$ SYM only at five loops, consistent with existing four-loop results. Our findings confirm that DR preserves supersymmetry for $\mathcal{N}=1, 2$ and $4$ SYM through the loop orders examined.

In this paper we explore the perturbative renormalization and study the classical dynamics of the bumblebee model coupled to quadratic gravity, a theoretical setting that allows the violation of Lorentz symmetry. Such a violation arises from a vector field whose potential is engineered to induce a nonzero vacuum expectation value (VEV), thereby leading to the emergence of a preferred direction in spacetime and, consequently, to the spontaneous breaking of Lorentz symmetry. Working in dimensional regularization and expanding the metric around flat space, we compute the one-loop divergent parts of the two-point functions of the bumblebee and graviton fields, with special emphasis on the role of Lorentz-violating insertions in internal lines. These results determine the counterterms required to renormalize the gravitational and bumblebee sectors in the presence of a preferred background direction, and make explicit how Lorentz-violating interactions feed back into the UV structure of quadratic gravity. On the classical side, we derive the field equations and identify exact solutions supported by bumblebee backgrounds. In particular, we show that the Schwarzschild geometry remains an exact solution for an appropriate bumblebee configuration, even in the presence of non-minimal couplings. We close with a discussion of the operator content suggested by the one-loop structure and of prospective extensions to cosmological and less symmetric backgrounds.

This thesis presents an extensive analysis of the behavior of topological solitons when one or more of their internal modes are activated. The first part of this manuscript is devoted to the study of the simplest topological solitons in (1+1) dimensions: kinks. Specifically, we investigate how these solutions emit radiation when one of their internal modes is initially excited, within the framework of the double $\phi^4$ model. The simplest kink solution in this theory exhibits a complex internal mode structure that depends on a coupling constant appearing in the potential governing the dynamics. We will show how the amplitude and frequency of the emitted radiation are affected by changes in this coupling constant. We also examine the dynamics of wobbling kink/antikink scattering when the kinks possess more than one internal mode. To this end, we study kink/antikink collisions in the context of the simplest kink solution arising in the MSTB model. This analysis sheds light on the resonant energy exchange mechanism, allowing energy transfer between internal modes and the translational mode. The second part of this thesis focuses on excited vortex solutions in (2+1) dimensions. We begin with a detailed study of the internal mode structure associated with vortex solutions in the Abelian-Higgs model. We demonstrate how the problem can be significantly simplified by choosing an appropriate angular dependence for the eigenfunctions. Furthermore, we investigate the radiation emitted by a vortex when its internal mode is initially activated. To achieve this, we extend the analytical techniques used in (1+1) dimensions to field theories defined in two spatial dimensions. This enables us to compute the radiation amplitude, its frequency, and the decay of the internal mode amplitude due to energy loss via radiation. All analytical results are contrasted with data from numerical simulations.

In this paper, we show that the Poisson algebras of cohomological and $K$-theoretic Coulomb branches of 3d $\mathcal{N}=4$ necklace quiver gauge theories provide Poisson structures and Hamiltonians that reproduce the equations of motion of the rational and hyperbolic spin Ruijsenaars-Schneider models, respectively. The construction is carried out in terms of monopole operators in the GKLO representation, also making the affine Yangian (and, in $K$-theory, quantum toroidal) superintegrability structure manifest. We conjecture that the Poisson algebras of elliptic Coulomb branches similarly reproduce the elliptic spin Ruijsenaars-Schneider model.

We derive exact, convergent representations of multiloop sunset Feynman integrals in two dimensions for arbitrary mass configurations and all loop orders valid for large Euclidean momentum. The integrals are expressed as sums of symmetric polynomials in logarithmic mass ratios, normalized by the external momentum squared, with coefficients determined by analytic series expansions. For the equal-mass case, we establish a dimension-raising relation expressing the $L$ loop sunset integrals in $D+2$ as the one in $D$ dimensions acted on a differential operator of order $L-1$. These representations are free of complicated transcendental functions, making them well-suited to both formal analysis and high-precision numerical evaluation. The two-dimensional results serve as boundary conditions for dimension-shifting relations, enabling systematic reconstruction of four-dimensional sunset integrals via analytic continuation to $D = 4 - 2\epsilon$.

In standard multi-field models, tachyonic isocurvature perturbations generally indicate the presence of an instability. We revisit the stability of some known counterexamples and show that, in a certain class of models that we call ultra slow-turn, an exponentially decreasing turn rate can shut off this potential instability. We argue that the stability of a given model can be correctly inferred by the total entropy perturbation, even if the effective mass squared of the isocurvature perturbation is negative. Several recent supergravity- or string-inspired models such as fibre inflation, SL(2,$\mathbb{Z}$) attractors and modular inflation fall into the ultra slow-turn class.

We show that ultraviolet information can be extracted from low-energy expansion coefficients, assuming analyticity and the absence of massless singularities. By reorganizing the low-energy expansion through an inverse Laplace transform and a controlled coarse-graining procedure, we make ultraviolet behavior accessible beyond the cutoff of the effective field theory. In particular, we determine the sign of the beta function and the associated dynamical scale directly from the low-energy expansion of a physical observable below the mass thresholds in QED and QCD-like theories.

We derive modular parametrizations for certain infinite series whose summands involve central binomial coefficients and higher-order harmonic numbers. When the rates of convergence are certain rational numbers, modularity allows us to reduce the corresponding series to special values of the Dirichlet $L$-functions. For example, we establish the following identities conjectured by Sun:\[\sum_{k=0}^\infty\binom{2k}{k}^3\left[ \mathsf H_{2k}^{(2)}-\frac{25}{92}\mathsf H_{ k}^{(2)} +\frac{735L_{-7}(2)-86\pi^{2}}{1104}\right]\frac{1}{4096^{k}}=0,\]\[\sum_{k=0}^\infty\binom{2k}k^3\left[\mathsf H_{2k}^{(3)}-\frac{43}{352}\mathsf H_k^{(3)}\right]\frac{42k+5}{4096^k}=\frac{555\zeta(3)}{77\pi}-\frac{32G}{11},\] where $ \mathsf H^{(r)}_k:= \sum_{0<n\leq k}\frac{1}{n^r}$, $ L_{-7}(2):= \sum_{n=1}^\infty\left(\frac{-7}{n}\right)\frac{1}{n^2}=\frac{1}{1^2}+\frac{1}{2^2}-\frac{1}{3^2}+\frac{1}{4^{2}}-\frac{1}{5^{2}}-\frac{1}{6^{2}}+\frac{1}{8^{2}}+\cdots $, $ G:= \sum_{n=0}^\infty\frac{(-1)^n}{(2n+1)^2}$, and $ \zeta(3):= \sum_{n=1}^\infty\frac1{n^3}$.

We construct the charged Hayward-anti-de Sitter (AdS) black hole (BH) with a cloud of strings (CS) and perfect fluid dark matter (PFDM), and analyze its extended thermodynamic phase structure. The Hayward parameter $g$ replaces the central singularity with a de Sitter (dS) core, while the CS parameter $a$ and the PFDM parameter $\beta$ encode astrophysically motivated matter content. Treating the cosmological constant as pressure, we derive the thermodynamic quantities, verify the Smarr relation, and establish $P$--$V$ criticality with a van der Waals (vdW)-like small-large BH phase transition and mean-field critical exponents. The Gibbs free energy (GFE) exhibits the characteristic swallowtail below the critical pressure. The Joule-Thomson (JT) expansion yields $T_i^{\rm min}/T_c \approx 0.247$, roughly half the Reissner--Nordström-AdS value. The parameters $g$ and $Q$ contract the cooling region, $\beta$ expands it, and $a$ reshapes it non-monotonically. A holographic heat engine with a rectangular cycle gives efficiencies $\eta = 0.362$--$0.396$ and Carnot benchmarking ratios $\eta/\eta_C = 0.625$--$0.791$ across six configurations. The CS parameter improves the engine efficiency by reducing the enthalpy at fixed thermodynamic volume, while the PFDM parameter degrades it by adding gravitational enthalpy without contributing to the mechanical work.

In this paper, we employ the quantum regression theorem, a powerful tool in the study of open quantum systems, to analytically study the correlation functions of an Unruh-DeWitt detector, which is an uniformly accelerated two-level quantum system, absorbing charges from an external classical coherent pulse. The system can thus be viewed as a relativistic quantum battery that interacts with the environment of its perceived particles, namely, the quanta of a massless scalar field. By considering the relativistic battery moving in Rindler spacetime, under Born-Markov approximation, we derive the Gorini-Kossakowski-Sudarshan-Lindblad master equation governing the evolution of the system's reduced density matrix. Moreover, we perform the Fourier transformation of the Wightman functions and use exponential regularisation to compute the functional forms appearing in the master equation. Next, we derive the evolution equations for the the single-time expectation values of the system's operators. We not only solve these equations to find out the single time averages, but also employ the quantum regression theorem to determine the two-time correlation functions of first and second order. We analyse them in details to explain the phenomenon of spontaneous emission and show analytically how the acceleration can enhance the associated dissipation. Furthermore, we address a special form of second order correlation function relevant to the context of photon bunching arising in Bose-Einstein statistics. Finally, we derive the spontaneous emission spectrum of the battery detector analytically, which in the long-time limit displays a well-defined Lorentzian line shape in the high frequency regime.

We investigate the thermodynamic topology of regular black holes with zero-point length using an extended first law that includes the zero-point length stored in the geometry. By treating the regularization scale $l_0$ as a thermodynamic variable, we analyze the Hessian geometry of the thermodynamic manifold and demonstrate that the vector field $\vec{\phi} = (T, \Psi)$, where $T$ is the temperature and $\Psi$ is the conjugate to $l_0$, never vanishes in the physical parameter space for $l_0 > 0$. This implies the absence of Morse critical points and a vanishing winding number ($W = 0$), indicating topological protection against the formation of naked singularities. Crucially, we show that in the singular limit $l_0 \to 0$, a non-zero winding number ($W = 1$) emerges, characterizing the Schwarzschild singularity as a topological defect. The conservation of this topological invariant under smooth evolution provides a rigorous topological formulation of the weak cosmic censorship conjecture: the presence of zero-point length not only regularizes the spacetime background but also enforces topological protection against the formation of singularities, preventing black hole-to-naked singularity transitions.

We study relativistic spin hydrodynamics on the hyperbolic $\kappa=-1$ flow background recently identified by Grozdanov. This background corresponds to an $SO(2,1)$-invariant, transversely expanding solution with finite spacetime support in Minkowski space, in contrast to the well-known Gubser flow $(\kappa=+1)$ which possesses $SO(3)$ symmetry and infinite transverse extent. Working within the formulation of perfect-fluid spin hydrodynamics, we derive the exact evolution equations for all spin components of the spin potential on the $\kappa=-1$ background. We find that the enhanced early-time expansion rate and the presence of a causal edge lead to a stronger localization of spin dynamics compared to the Gubser case. Remarkably, the azimuthal component of the spin potential oscillates as it decays in the forward lightcone, in stark contrast to the Gubser flow. Thus, our results establish the $\kappa=-1$ flow as a distinct and physically meaningful benchmark for studying spin dynamics in expanding relativistic fluids with finite spacetime support.

We present the variational action principle for initial value problems in classical, conservative-force point particle mechanics. We rigorously derive this formulation by taking the classical limit of the Schwinger-Keldysh expression for the time dependence of the expectation value for operators in quantum mechanics. We clarify the connection between the variation of the position and the variation of the velocity of a particle when implementing Hamilton's Principle in deriving the Euler-Lagrange Equations. We show that both the plus and minus Keldysh paths (of the average and difference of the forward/backward paths) have classical paths and fluctuations -- unlike the common perception that the minus path provides the fluctuations around the single classical solution given by the plus path -- and that the fluctuations of both paths are crucial for the correct normalization of the classical limit. The classical limit yields "initial conditions" and equations of motion for the minus paths such that the unique classical solution for the minus paths is that they are identically zero, and, fascinatingly, that the minus paths' solution propagates backwards in time; thus one does not need to set the minus paths to zero by hand when taking the classical limit of the Schwinger-Keldysh formalism. We note implications for the classical and quantum mechanics of non-holonomic constraints and quantum field theories with gauges dependent on the derivatives of the fields.

Conventional Boltzmann--Gibbs statistical mechanics successfully describes systems with weak to moderate correlations, where the number of accessible configurations $W(N)$ grows exponentially with the number of degrees of freedom~$N$. However, this framework breaks down for systems with strong correlations or long-range interactions, for which the configuration space exhibits non-exponential growth. While numerous generalized entropies have been proposed to address this limitation, a coherent link to classical thermodynamic laws has remained elusive. Here, we propose group entropies as a unifying framework, defining universality classes of entropies through the asymptotic scaling of $W(N)$, each yielding an extensive entropy. We show that this approach provides the basis for a consistent thermodynamic formulation beyond the Boltzmann--Gibbs paradigm. In particular, by expressing these entropies in terms of thermodynamic state variables and taking the thermodynamic limit, we demonstrate their consistency with classical thermodynamics, in close analogy to the emergence of the Clausius entropy from the Boltzmann--Gibbs formalism. Focusing on the zeroth thermodynamic law, we identify the empirical temperature and, by using Carathéodory's formulation of the second law, we derive the associated absolute temperature. As an application of the thermodynamic framework obtained, we analyze black-hole thermodynamics using the group entropy class corresponding to stretched-exponential behavior of $W(N)$. In particular, we show that a hallmark property of black holes -- their negative specific heat -- emerges naturally within this framework while the entropy remains extensive. This result holds for the stretched-exponential entropies associated with both the Bekenstein--Hawking and Barrow entropy scalings.

Supergravity provides the natural supersymmetric framework for early universe cosmology. A broad class of inflationary models in no-scale supergravity yields tree-level predictions for cosmic microwave background (CMB) observables that closely resemble those of the Starobinsky $R + R^2$ model. Using results from global supersymmetry and supergravity, we analyze radiative corrections in models with canonical and non-canonical kinetic terms, focusing particularly on Starobinsky-like no-scale supergravity models. We derive conditions on the superpotential that keep the gravitino mass finite during inflation and ensure that loop-induced corrections to the Kähler potential remain either finite or subdominant relative to the tree-level potential. We show that in some models, most notably the original no-scale supergravity model with a Wess-Zumino superpotential, radiative corrections grow at large inflaton field values and can dominate the inflationary dynamics, rendering unreliable the model predictions for CMB data. However, we identify a class of no-scale Starobinsky-like models, including the Cecotti model, in which radiative corrections remain very small for inflaton field values $\lesssim 8$ (in Planck units), preserving the agreement of the tree-level predictions with Planck CMB data.

Under a time-dependent perturbation it is common to calculate the transition probability in going from from one eigenstate to another eigenstate of a quantum system. In this work we study the transition in going from a \textit{linear superposition of eigenstates} to an eigenstate under a delta-function pulse (which acts at $t=0$). We consider a two-level system with energy levels $E_1$ and $E_2$ and solve the coupled set of first order equations to obtain exact analytical expressions for the coefficients $c_1(t>0)$ and $c_2(t>0)$ of the final state. The expressions for the final coefficients are general in the sense that they are functions of the interaction strength $\beta$ and the coefficients $\alpha_1$ and $\alpha_2$ of the initial superposition state which are free parameters constrained only by $|\alpha_1|^2+ |\alpha_2|^2=1$. This opens up new possibilities and in particular, allows for a ``collapse" scenario. We obtain a general analytical expression for the transition probability $P_{\alpha_1,\alpha_2 \to 2}$ in going from an initial superposition state to the second eigenstate. Armed with this general expression we study some interesting special cases. With a delta-function pulse, the transitions are abrupt/instantaneous and we show that they do not depend on the energy gap $E_2-E_1$ and hence on the relative phase between the two eigenstates. For specific multiple values of the interaction strength $\beta$, we show that the system ends up in a definite eigenstate i.e. probability of unity. Such a transition can be viewed as a ``collapse" since a superposition of states transitions abruptly to a definite eigenstate. The collapse of the wavefunction is familiar in the context of a measurement. Here it occurs via a delta-function pulse in Schrödinger's equation. We discuss how this differs from a collapse due to a measurement.

In astrophysics, extreme mass ratio inspiral (EMRI) systems, which consist of a central supermassive black hole and a stellar-mass compact object (SCO), are typically embedded in galactic dark matter (DM) halos. This dark matter environment inevitably affects the orbital dynamics of the SCO and the gravitational wave (GW) signals emitted by the system. In this work, we select two typical dark matter halo profiles -- the Navarro-Frenk-White (NFW) and Beta models -- to systematically investigate their specific impacts on the long-term orbital evolution of the SCO. By incorporating three dissipative mechanisms -- dynamical friction, accretion, and gravitational radiation reaction -- our results demonstrate that, compared to a pure vacuum medium, the presence of a dark matter halo significantly alters the trajectories of precessing orbits, the dynamical evolution of orbital parameters, and the waveforms and phases of the emitted gravitational waves. Due to the strong accretion effect within the NFW model, the energy flux exhibits a distinctive "cusp" feature, marking a reversal from net energy loss to gain at a specific semi-latus rectum, which is a phenomenon absent in the Beta model. Although short-term observations may not be sufficient to distinguish between the NFW and Beta models, their differences become evident over long-term orbital evolution. The gravitational waveforms computed using the NFW and Beta models exhibit a phase shift, which could be detectable in high-density DM environments. This phase shift becomes even more pronounced for higher eccentric orbits and longer observation times. These results offer a theoretical framework for probing environmental effects on EMRIs across different dark matter models using future space-based gravitational wave observatories.

We develop a framework for testing quantum gravity through the stochastic gravitational-wave background produced by evaporating near-Planck-mass primordial black holes. Because gravitons free-stream from the emission region without rescattering, they preserve a direct spectral record of the black-hole temperature--mass relation $T(M)$, a relation that is erased for all other Hawking-radiated species by rapid thermalization. We translate six representative phenomenological beyond-semiclassical frameworks (the generalized uncertainty principle, loop quantum gravity, noncommutative geometry, asymptotic safety, string/Hagedorn physics, and tunneling backreaction) into distinct $T(M)$ parametrizations and compute the resulting gravitational wave spectra numerically. Modifications that suppress $T(M)$ shift the spectral peak by up to ten decades in frequency, in some cases into the sensitivity bands of next-generation interferometers or resonant-cavity detectors, while models imposing a hard evaporation cutoff produce distinctive peak morphologies that discriminate between quantum-gravity scenarios. We further discuss the impact of different choices for post-inflationary conditions in the very early universe. We find that the relative spectral displacement between the standard Hawking prediction and any modified model is cosmology-independent, hence spectral shape rather than absolute peak frequency provides the cleanest probe of Planck-scale physics.

An axion-like field coupled to an Abelian gauge field provides one of the simplest inflationary models that is free from the eta problem and possesses an efficient reheating mechanism. For sufficiently large coupling, this system enters a regime of strong gauge-field backreaction, exhibiting rich and intricate dynamics. In this work, we employ a semi-analytical method, the gradient-expansion formalism, to perform a comprehensive parameter scan and determine the precise conditions under which backreaction sets in. Previous studies have shown that the Anber-Sorbo solution, in which the potential-gradient force acting on the axion is balanced by Hubble friction and gauge-field backreaction, is unstable. Here, we broaden the parameter space and identify a new region in which the Anber-Sorbo solution remains stable despite strong backreaction. Although our analysis is restricted to a homogeneous axion field and to perturbations that depend only on time, we expect that this stability property can be extrapolated to generic time- and space-dependent perturbations. This newly identified region therefore represents a distinct type of backreaction - stable backreaction - which may not be accompanied by the rapid growth of perturbations. We further investigate the nonlinear behavior of solutions in the backreaction regime in a toy model (de Sitter, constant potential slope, no axion gradients), identifying a supercritical Hopf bifurcation at the onset of instability, a nontrivial limit cycle in the unstable regime, and burst-like oscillatory dynamics. Finally, we present a more stringent criterion for the onset of (unstable) backreaction, based on crossing the instability threshold, and apply this criterion to two benchmark inflationary models.

We investigate critical phenomena in the $O(2)$ models using symmetry-twisted partition functions that can be efficiently computed within the tensor renormalization group framework. We first demonstrate, taking the three-dimensional model as an example, that symmetry-twisted partition functions detect the spontaneous breaking of global continuous symmetry. We then consider the same model in two dimensions, where the Berezinskii--Kosterlitz--Thouless (BKT) transition occurs. Since symmetry-twisted partition functions directly provide the helicity modulus at a finite twist angle, we determine the BKT transition point. These results are presented based on Ref.~\cite{Akiyama:2026dzg}. Finally, in addition to the original paper~\cite{Akiyama:2026dzg}, we apply this approach to the two-dimensional generalized $O(2)$ model and confirm that it successfully identifies the phase transitions between the ferromagnetic and nematic phases, as well as between the nematic and paramagnetic phases.

In the present paper we consider anisotropic cosmological vacuum solutions in (4+1) dimensional general quadratic gravity. In particular, we present a solution with 3 equal and 1 different Hubble parameters, and study its stability. We show that for a certain range of coupling constants this solution is stable. This means that initially totally anisotropic 4-dim Universe can evolve naturally to a product of 3-dim isotropic subspace and 1-dim space. By numerical integration of equations of motion we construct bassin of attraction of this solution which covers part of the initial conditions space with non-zero measure.

The spontaneous breaking of $SO(10)$ via flipped $SU(5)$ to the Standard Model yields a novel scenario in which the superheavy topologically stable GUT monopole carrying a single unit ($2\pi/e$) of Dirac magnetic charge emerges from the merger of a confined but topologically distinct monopole-antimonopole pair that are pulled together by a string. The $SO(10)$ breaking via the subgroup $SU(4)_c\times SU(2)_L\times SU(2)_R$, following a similar reasoning, produces a topologically stable monopole that carries two units ($4\pi/e$) of Dirac charge. We explore the cosmological consequences of this scenario by assuming that the monopoles and strings experience a limited number of inflationary $e$-foldings, before re-entering the horizon and ultimately forming a network of quasi-stable strings bounded by monopole-antimonopole pairs. We identify regions of the parameter space that yield an observable number density of the GUT monopole from the collapse of the appropriate string segments. The gravitational waves emitted by these quasi-stable cosmic strings lie in the Hz to kHz range, which can be tested in a number of proposed and ongoing experiments.

We propose a lattice-ready entanglement observable for QCD hadrons: the vacuum-subtracted radius flow of the ball Rényi entropy, $\mathfrak{s}_n(R;h)\equiv R\,\partial_R\Delta S_n(B_R;h)$, defined via the Euclidean replica cut-and-glue construction in a rest-frame momentum-projected one-hadron state, with spin averaging performed at the level of the final flow. In the continuum, varying $R$ at fixed shape is equivalent to a Weyl rescaling, so the flow is trace selected and admits a surface-plus-remainder organization on the entangling sphere. We use this to formulate a lattice stability test of boundary dominance: fit the measured flow on local $R$ windows to a low-curvature remainder plus a small template basis built from hadronic gravitational form factors (GFFs). The two endpoint templates are the spin-0/trace shape $\mathfrak{t}_h^{(0)}(R)=R^3\rho_S(R)$ constructed from $A^S(t)$ and a spin-2/TT proxy $\mathfrak{t}_h^{(2)}(R)=R^3\rho_A(R)$ constructed from $A(t)$, together with the mixed family $\mathfrak{t}_h^{\rm mix}(R;c_0,c_2)=c_0\mathfrak{t}_h^{(0)}(R)+c_2\mathfrak{t}_h^{(2)}(R)$. A soft-wall AdS/QCD appendix shows that the pole-subtracted integrated trace--energy correlator closes on this same $\{A^S,A\}$ basis and supplies a model-dependent benchmark ratio for $c_0/c_2$; for lattice comparison the coefficients are left free and extracted from data. For representative nucleon dipole inputs, the pure endpoints predict distinct single-extremum scales, $R_{\rm EE}^{(0)}\sim0.84~\mathrm{fm}$ and $R_{\rm EE}^{(2)}\sim0.43~\mathrm{fm}$, enabling discrimination among scalar control, spin-2 control, and genuine mixing through the turning-point location, the sign change of the slope across it, and the fitted ratio of template weights.

In the present work we construct a novel generative architecture for systems with complex probability distributions. In general, these sampling tasks come with two challenges: resolving sign problems and efficient sampling. The architecture is based on physics-informed kernels (PIKs) introduced in arXiv:2510.26678, and aims at resolving both challenges. Key to the complex PIK-architecture is its probability-weight preserving property, which allows us to map the sampling task to one on a sign-problem free manifold with a simple distribution and efficient sampling. The potential of this novel architecture is demonstrated within applications to zero-dimensional field theories with complex couplings, as well as the real-time evolution of the quantum-mechanical harmonic oscillator.

We calculate the renormalization constants of the N=1, N=2, N=4 supersymmetric Yang-Mills theories in an arbitrary covariant gauge in the dimensional reduction scheme up to three loops. We have found, that the beta-functions for N=1 and N=4 SYM theories are the same from the different triple vertices. This means that the dimensional reduction scheme works correctly in these models up to third order of perturbative theory.

Despite the absence of a lightcone structure, some solutions of Carroll gravity show black hole-like behaviour. We define Carroll black holes as solutions of Carroll gravity that exhibit Carroll thermal properties and have a Carroll extremal surface, notions introduced in our work. The latter is a Carroll analogue of a Lorentzian extremal surface. As examples, we discuss the Carroll versions of Schwarzschild, Reissner-Nordstroem, and BTZ black holes and black hole solutions of generic 1+1 dimensional Carroll dilaton gravity, including Carroll JT and Carroll Witten black holes.

We study the interplay between magic and entanglement in quantum many-body systems. We show that non-local magic, which is supported by the quantum correlations is lower bounded by the non-flatness of entanglement spectrum and upper bounded by the amount of entanglement in the system. We then argue that a smoothed version of non-local magic bounds the hardness of classical simulations for incompressible states. In conformal field theories, we conjecture that the non-local magic should scale linearly with entanglement entropy but sublinearly when an approximation of the state is allowed. We support the conjectures using both analytical arguments based on unitary distillation and numerical data from an Ising CFT. If the CFT has a holographic dual, then we prove that the non-local magic vanishes if and only if there is no gravitational back-reaction. Furthermore, we show that non-local magic is approximately equal to the rate of change of the minimal surface area in response to the change of cosmic brane tension in the bulk.

Double-scaled SYK (DSSYK) is known to have an underlying quantum group theoretical description. We precisely pinpoint the quantum group structure, improving upon earlier work in the literature. This allows us to utilize this framework for bulk gravitational applications. We explain bulk discretization in DSSYK from the underlying irreducibility of the representations. We derive trumpet and brane amplitudes using character insertions of the quantum group, simplifying earlier calculations. Most importantly, we factorize the bulk Hilbert space dual to DSSYK in the quantum group description using a complete set of edge degrees of freedom living at a bulk entangling surface. An analogous treatment for $\mathcal{N}=1$ DSSYK is provided in the same quantum group theoretical framework.

We develop a covariant Lagrangian formulation for a time reversal symmetry broken, minimally relativistic three dimensional Weyl superconductor that preserves continuous chiral invariance in the chiral limit. Within this framework, the FFLO pairing spontaneously breaks the axial $U(1)_A$ symmetry, giving rise to distinct collective excitations. Using the Nambu Jona Lasinio approach, we identify a pseudo scalar Nambu Goldstone mode (This mode is absent for conventional BCS internode pairing) that acquires a small mass under explicit chiral symmetry breaking and couples to gauge fields through the axial anomaly, closely analogous to the neutral pion decay in QCD. Although this anomaly induced decay is strongly suppressed in the bulk by the Meissner effect, it may occur via surface electromagnetic fields. Our analysis also predicts additional vector and axial vector collective modes associated with the broken $U(1)_A$ symmetry, providing a unified description of collective excitations in Weyl superconductors and their correspondence to mesonic modes in QCD.

The one-loop correction to eleven-dimensional supergravity involves a cubically divergent term $t_8t_8R^4$, with four Riemann tensors. A similar term (with finite coefficient) has been argued to be present in the M-theory effective action. It is expected to reduce to a similar one-loop term present in the type IIA effective action. This has previously been verified in the NSNS sector at the 4-point level. Here we extend this result to couplings of NSNS and RR fields, which have been computed using the pure spinor formalism. In particular, we check all couplings of RR fields to the dilaton as well as all couplings involving the metric and RR three-form. Correcting some minor mistakes in the literature we find complete agreement. We also give a complete analysis of 4-point terms in eleven dimensions computed previously from superparticle amplitudes and present a very simple form for these.

In this work, we study nonconformally Ricci-flat gravitational instantons in four-dimensional Conformal Gravity, both in vacuum and in the presence of nonlinear conformal matter. First, the one-parameter extension of the Kerr-NUT-AdS metric is analyzed. We obtain their conserved charges by using the Noether-Wald formalism. It turns out that they receive corrections from the linear modes present in Conformal Gravity, which are properly identified. Then, we perform the analytic continuation into the Euclidean section and find the curve in parameter space along which this solution becomes regular and globally (anti)self-dual. Using the Dunajski-Tod theorem, we show that the self-dual metric is not conformally Ricci-flat. Then, the backreaction of nonlinear conformal matter is considered. In particular, we find new gravitational instantons in the presence of conformally coupled scalar fields and ModMax electrodynamics. We compute the partition function and conserved charges, which turn out to be finite by virtue of the conformal invariance of the theory. As a byproduct, we also obtain a generalization of the Riegert metric dressed with nonlinear conformal matter as a particular limit of these instantons. For all cases, we analyze the global properties, the curve in parameter space where the solutions are (anti)-self-dual, and the on-shell Euclidean action, among other features.

We provide arguments indicating that the semiclassical Einstein equations follow from quantum relative entropy and its proportionality to an area variation. Using modular theory, we establish that the relative entropy between the vacuum state and coherent excitations of a scalar quantum field on a bifurcate Killing horizon is given by the energy flux across the horizon. Under the assumption of the Bekenstein-Hawking entropy-area formula, this energy flux is proportional to a variation in the surface area of the horizon cross section. The semiclassical Einstein equations follow automatically from this identification. Our approach provides a quantum field theoretic generalization of Jacobson's thermodynamic derivation of the Einstein equations, replacing classical thermodynamic entropy with the well-defined quantum relative (Araki-Uhlmann) entropy. This suggests that quantum information plays a central role in what is often seen as a zeroth order approximation of a theory of quantum gravity, namely quantum field theory in curved spacetimes.

We provide a detailed derivation of the Schwarzian modes in the full geometry of the Bañados-Teitelboim-Zanelli (BTZ) black hole at finite temperature, establishing the precise conditions under which they emerge from the general solution, thereby clarifying the absence of rotational modes in the full geometry. In addition, we demonstrate that the same modes can be recovered through a purely geometric Kerr-Schild construction. This equivalent approach offers a new geometric understanding of the Schwarzian sector and highlights the correspondence between perturbative and pure geometric approaches, additionally it provides a connection with double copy.

Pursuing our analysis of [1], we study the gravitational solution space around a null hypersurface in the bulk of spacetime, such as a black hole or a cosmological horizon. We discuss the corresponding characteristic initial value problem both in the metric and Newman-Penrose formalisms, and establish an explicit dictionary between the two. This allows us to identify Weyl-covariant structures in the solution space, including hierarchies of recursion relations encoding the flux-balance laws. We then establish a correspondence between the gravitational phase space at null infinity and the subleading phase space around the null hypersurface at finite distance. This connection is naturally formulated within the Newman-Penrose formalism by performing a partially off-shell conformal compactification and identifying the analogue of the Ashtekar-Streubel symplectic structure in the radial expansion near the null hypersurface. Using this framework, we identify the celestial $Lw_{1+\infty}$ symmetries in the subleading phase space at finite distance by constructing their canonical generators and imposing self-duality conditions. This allows us to define a notion of covariant radiation, whose absence gives rise to an infinite tower of conserved charges, revealing physical quantities relevant to observers near black hole or cosmological horizons. As a concrete illustration, we consider the case of the self-dual Taub-NUT black hole.

We consider realizations of a gauged B-L symmetry in the context of the Dark Dimension scenario, where the SM lives on a codimension one brane in 5d spacetime. The B-L can naturally be a bulk gauge symmetery leading to a global symmetry on the SM brane, and have its gauge anomaly canceled by charged bulk modes. This naturally leads to the existence of 3 right-handed neutrinos propagating in the dark dimension. Allowing for Higgsing of B-L by a bulk scalar at the Higgs scale, results in a massive gauge field with $m_{B-L}\sim 100$ GeV and weak coupling $g_{B-L}\sim 10^{-10}$ which is allowed by current bounds. The model also predicts a natural matching $m_\nu\sim m_{KK}\sim\Lambda^{1/4}$, thereby providing a theoretical explanation for the observed coincidence between neutrino masses and the Dark Energy scale. It also predicts a tower of sterile right-handed neutrinos in the $keV$ mass range.

In \cite{salvio}, inspired by the works \cite{pauli}-\cite{donogue}, a prescription for calculating the correlation functions in Quadratic Gravity \cite{stelle1}-\cite{stelle2} was presented and further exploited in \cite{salvio2}-\cite{salve}. This procedure does not enter in conflict with unitarity. The corresponding Hamiltonian quantization is based on a covariant and contra-variant distinction in the non positive definite metric in the space of states \cite{gross}. The Gauss-Ostrogradsky method for higher order theories defines two momentum densities $P_1$ and $P_2$ and two coordinate densities $Q_1$ and $Q_2$, one pair is standard, the other ghost like. The approach in \cite{salvio} involves the continuation $P_2\to i P_2$ and $Q_2\to i Q_2$ of the ghost variables acting on kets $|>$ after taking mean values. In the present work, following \cite{yomismo}, the LSZ rules are derived, with a formalism adapted to full quartic or higher order theories. The derivation of these rules is possible only after the second quantization of the free theory. This is considered here, in a more general setting than \cite{yomismo}. It includes a Gupta-Bleuler characterization of the physical states. The effective action $\Gamma$ can be calculated following \cite{stelle1}, and can be constrained by the Slavnov-Taylor identities \cite{Slavnov}-\cite{Taylor}.

We revisit the strong CP problem from the viewpoint of the infrared structure of non-Abelian gauge theories. In Yang-Mills theory, motion between topologically inequivalent vacua may be described in terms of a compact collective coordinate associated with the Chern-Simons number. Implementing an adiabatic separation between slow topological modes and fast gluonic fluctuations leads to a reduced Born-Oppenheimer Hamiltonian governing the infrared dynamics. We show that the physical parameter entering this reduced Hamiltonian is not the bare vacuum angle $\theta$, but an effective holonomy $\theta_{\rm eff}$ that includes a Berry phase induced by the fast gluonic sector. The induced holonomy becomes a self-consistent response function of the infrared dressing, leading to a nonperturbative renormalization group flow for $\theta_{\rm eff}$. This infrared flow admits CP-invariant fixed points toward which the effective vacuum angle is dynamically driven in the infrared limit. In this framework, CP violation is not forbidden by the fundamental theory but becomes dynamically suppressed along the infrared flow generated by adiabatic dressing. The strong CP problem is thus realized as a nonperturbative infrared relaxation mechanism governed by the Berry response of the fast gluonic sector, without the introduction of additional dynamical fields.

In this note, we give a non-perturbative construction of a lightlike domain wall separating IIA and IIB string theories in 10D in the framework of discrete light-cone quantization (DLCQ). In this setting, generalizations of the BFSS conjecture relate the 10D flat space limit to matrix string theories (MSTs) for IIA and IIB. The former is equivalent to the large-$N$ limit of 2D Super Yang-Mills theory, while the latter is the large-$N$ limit of 3D ABJM theory with $\pm 1$ Chern-Simons levels. Our construction requires the string coupling to vanish at the location of the wall, and we show that BPS IIA $D0$-branes become non-BPS IIB $D0$-branes as they cross it, as anticipated in \cite{Heckman:2025wqd}.

These lectures present a general critical assessment of various frameworks for quantum gravity, with particular emphasis on string theory. The topics discussed cover field-theoretical approaches to quantum gravity, anomalies, bosonic and fermionic string theories, as well as some aspects of string phenomenology and black hole physics.

We analyze the confinement/deconfinement transition of pure Yang-Mills theories within the framework of the center-symmetric Landau gauge supplemented by a Curci-Ferrari mass term that models the effect of the associated Gribov copies in the infrared. In addition to providing details for earlier one-loop calculations in that framework, we explore how the results depend on the renormalization scale and/or on the renormalization scheme. We find that the predicted values for the transition temperatures of SU($2$) and SU($3$) Yang-Mills theories are similar in both schemes and are little sensitive to the renormalization scale $\mu$ over a wide range of values including the standard range $\smash{\mu\in[\pi T,4\pi T]}$. These values are also close both to those obtained from a minimal sensitivity principle and to those of lattice simulations, especially in the SU($3$) case. These results further confirm the good behavior of perturbative calculations within the Curci-Ferrari model and support the adequacy of the latter as an effective description of Yang-Mills theories in the infrared. We perform a similar analysis for the spinodal temperatures in the SU($3$) case and for the Polyakov loop, the order parameter associated to the breaking of center symmetry.

We study stratifications of regions in the space of symmetric matrices. Their points are Mandelstam matrices for momentum vectors in particle physics. Kinematic strata in these regions are indexed by signs and rank two matroids. Matroid strata of Lorentzian quadratic forms arise when all signs are non-negative. We characterize the posets of strata, for massless and massive particles, with and without momentum conservation.

We identify an observable that could operate as a probe of the quark versus hadron content of a bath of quarks and gluons at finite temperature and chemical potential. To this purpose, we relate the Polyakov and anti-Polyakov loops, which determine how energetically costly it is to bring an external static quark or antiquark probe into the thermal bath, to the ability of that medium to provide favorable conditions for the formation of meson-like or baryon-like configurations that would screen the probes.

We study the thermodynamics of Einstein-Power-Yang-Mills AdS black holes via the Euclidean path integral method, incorporating appropriate boundary and counterterms. By analyzing unstable timelike and null circular geodesics, we demonstrate that their Lyapunov exponents reflect the thermodynamic phase structure obtained from the Euclidean action. Specifically, the small-large black hole phase transition, analogous to a van der Waals fluid, is signaled by a discontinuity in the Lyapunov exponent. Treating this discontinuity as an order parameter, we observe a universal critical exponent of $1/2$, consistent with mean-field theory. These results extend previous insights from black hole spacetimes with Abelian charges to scenarios involving nonlinear, non-Abelian gauge fields, highlighting the interplay between black hole thermodynamics and chaotic dynamics.

We provide a pedagogical introduction to the concepts underlying black hole information loss, intended for readers familiar with special relativity and quantum mechanics. We emphasize that there is no paradox of information loss, and that proposals suggesting deviations from well-established theories at arbitrary regimes are inherently contradictory.

We introduce a novel mechanism -- Magnetically Arrested Transmutation (MAT) -- which could be a viable model to account for the observed over-representation of magnetic white dwarfs (WDs) near the Galactic centre (GC), and the presence of a magnetar as opposed to the absence of ordinary pulsars in the same region. In this scenario, compact stars accumulate asymmetric or non-self-annihilating dark matter particles, eventually forming an endoparasitic black hole (EBH) of initial mass $M_0$ at their core. Although such EBHs generally grow by accreting host matter, we show that sufficiently strong core magnetic fields can establish pressure equilibrium, thereby stalling further accretion and halting the star's transmutation into a black hole. We derive the conditions for this MAT to occur, identifying a critical parameter $\beta$, that encapsulates the interplay between the magnetic field strength, host matter density, and EBH mass. For $0 < \beta \leq 4/27$, the growth of the EBH is arrested, limiting its final mass ($M_{\rm f}$) to $M_0 <M_{\rm f} \leq 3/2M_0$, whereas for $\beta > 4/27$, full transmutation may ensue. We argue that highly magnetized WDs may survive near the GC due to the MAT mechanism, as do high-spin ordinary WDs, despite hosting a central EBH. We also speculate a possibility that the magnetar PSR J1745-2900 survives near the GC due to the MAT mechanism. Overall, the MAT framework may explain an elevated population of magnetic WDs in dense dark matter environments, and hence could be tested and should have implications for understanding dark matter and compact objects.

Quantum field simulators provide unique opportunities for investigating the dynamics of quantum fields through tabletop experiments. A primary drawback of standard encoding schemes is their rigidity: altering the theory, its coupling geometry, metric structure, or simulation time typically requires redesigning the experimental setup, which imposes strong constraints on the types of dynamics and theories that can be simulated. Here, we introduce the Optical Time Algorithm (OTA) as a unifying framework, enabling the efficient simulation of large classes of free quantum field dynamics using a single optical circuit design that separates the time from the Hamiltonian's structure. By modifying the parameters of the optical elements, our method allows us to engineer timescales, coupling graphs, spacetime metrics, and boundary conditions, thereby facilitating the implementation of relativistic and non-relativistic, real- and complex-valued, short- and long-range quantum field theories on both flat and curved spacetimes. We exploit the OTA's configurability to investigate the spreading of quantum correlations in space and time for theories with continuously varying coupling ranges. Relevant features predicted by quantum field theory can be observed on systems of $10$ to $20$ modes, which paves the ground for experimental implementations.

Large Momentum Effective Theory (LaMET) provides a general framework for computing the multi-dimensional partonic structure of the proton from first principles using lattice quantum chromodynamics (QCD). In this effective field theory approach, LaMET predicts parton distributions through a power expansion and perturbative matching of a class of Euclidean observables -- quasi-distributions -- evaluated at large proton momenta. Recent advances in lattice renormalization, such as the hybrid scheme with leading-renormalon resummation, together with improved matching kernel that incorporates higher-loop corrections and resummations, have enhanced both the perturbative and power accuracy of LaMET, enabling a reliable quantification of theoretical uncertainties. Moreover, the Coulomb-gauge correlator approach further simplifies lattice analyses and improves the precision of transverse-momentum-dependent structures, particularly in the non-perturbative region. State-of-the-art LaMET calculations have already yielded certain parton observables with important phenomenological impact. In addition, the recently proposed kinematically enhanced lattice interpolation operators promise access to unprecedented proton momenta with greatly improved signal-to-noise ratios, which will extend the range of LaMET prediction and further suppress the power corrections. The remaining challenges, such as controlling excited-state contamination in lattice matrix elements and extracting gluonic distributions, are expected to benefit from emerging lattice techniques for ground-state isolation and noise reduction. Thus, lattice QCD studies of parton physics have entered an exciting stage of precision control and systematic improvement, which will have a broader impact for nuclear and particle experiments.

This document serves as a conceptual and practical introduction to Strong-Field Quantum Electrodynamics (SFQED), written from the standpoint of experimental physicists. Rather than providing a comprehensive theoretical review, the document focuses on the core ideas, terminology, and challenges in SFQED that are most relevant to experimental design and interpretation. Our goal is to offer a first point of contact with the subject, bridging the gap between foundational theory and hands-on experimental work, and complementing more formal literature in the field.

Studies of quantum field entanglement in de Sitter space based on the von Neumann entropy of local patches have concluded that curvature enhances entanglement between regions and their complements. Similar conclusions about entanglement enhancement have been reached in analyses of Fourier modes in the cosmological patch of de Sitter space. We challenge this interpretation by adopting a fully local approach: examining entanglement between pairs of field modes compactly supported within de Sitter's cosmological patch. Our approach is formulated in terms of the properties of a metric tensor and an associated complex structure induced by the Bunch-Davies vacuum on the classical phase space. We find that increasing curvature increases correlations between local modes but, somewhat counterintuitively, decreases their entanglement. Our methods allow us to characterize how entanglement is spatially distributed, revealing that a cosmological constant, even if tiny, qualitatively alters the vacuum's entanglement structure. We show that our results are compatible with previous entropy-based studies when properly interpreted. Our findings have implications for entanglement between observables generated during cosmic inflation.