We construct postcarrollian gravity models in two, three, and four spacetime dimensions by applying algebraic expansion methods. As a byproduct, we present the most general postcarrollian 2d dilaton gravity model, construct its solutions and discuss some boundary aspects, including Schwarzian-type boundary actions. In 3d, we propose Brown-Henneaux-like boundary conditions, generalizing a corresponding Carrollian analysis, and derive the postcarrollian asymptotic symmetry algebra with its central extensions.

We give a brief, incomplete, and idiosyncratic review of the early years of supergravity in superspace as our contribution to the book Half a Century of Supergravity edited by Anna Ceresole and Gianguido Dall'Agata.

This paper develops a framework for the Hamiltonian quantization of complex Chern-Simons theory with gauge group $\mathrm{SL}(2,\mathbb{C})$ at an even level $k\in\mathbb{Z}_+$. Our approach follows the procedure of combinatorial quantization to construct the operator algebras of quantum holonomies on 2-surfaces and develop the representation theory. The $*$-representation of the operator algebra is carried by the infinite dimensional Hilbert space $\mathcal{H}_{\vec{\lambda}}$ and closely connects to the infinite-dimensional $*$-representation of the quantum deformed Lorentz group $\mathscr{U}_{\mathbf{q}}(sl_2)\otimes \mathscr{U}_{\widetilde{\mathbf{q}}}(sl_2)$, where $\mathbf{q}=\exp[\frac{2\pi i}{k}(1+b^2)]$ and $\widetilde{\mathbf{q}}=\exp[\frac{2\pi i}{k}(1+b^{-2})]$ with $|b|=1$. The quantum group $\mathscr{U}_{\mathbf{q}}(sl_2)\otimes \mathscr{U}_{\widetilde{\mathbf{q}}}(sl_2)$ also emerges from the quantum gauge transformations of the complex Chern-Simons theory. Focusing on a $m$-holed sphere $\Sigma_{0,m}$, the physical Hilbert space $\mathcal{H}_{phys}$ is identified by imposing the gauge invariance and the flatness constraint. The states in $\mathcal{H}_{phys}$ are the $\mathscr{U}_{\mathbf{q}}(sl_2)\otimes \mathscr{U}_{\widetilde{\mathbf{q}}}(sl_2)$-invariant linear functionals on a dense domain in $\mathcal{H}_{\vec{\lambda}}$. Finally, we demonstrate that the physical Hilbert space carries a Fenchel-Nielsen representation, where a set of Wilson loop operators associated with a pants decomposition of $\Sigma_{0,m}$ are diagonalized.

This article is a write-up of the talk given in one of the mini-symposia of the 2024 European Congress of Mathematicians. I will explain some basics of the representation theory underlying Spin(10) and SU(5) Grand Unified Theories. I will also explain the characterisation of the Standard Model gauge group G_SM as a subgroup of Spin(10) that was developed in [1]. Thus, the symmetry breaking required to obtain G_SM can be seen to rely on two suitably aligned commuting complex structures on R10. The required complex structures can in turn be encoded in a pair of pure spinors of Spin(10). The condition that the complex structures are commuting and suitably aligned translates into the requirement that the respective pure spinors are orthogonal and that their sum is again a pure spinor. The most efficient description of spinors, and in particular pure spinors of Spin(10) is via the octonionic model of the latter, and this is how octonions enter the story.

In this paper we investigate and propose new dualities involving 2d gauge theories with $\mathcal{N}=(0,2)$ supersymmetry. In the first part of the paper we focus on $\mathrm{SU}(n)$ gauge theories with two antisymmetric chirals. The gauge theories are non-anomalous if we consider, in addition to such matter content, $n_f$ fundamental and $n_a$ antifundamental chirals, provided the constraint $n_f+n_a=4$. By exploring the five possibile scenarios arising from this constraint we provide in each case evidences of a dual LG description, by matching the 't Hooft anomalies and deriving the relation between the elliptic genera in terms of other more fundamental dualities. In the second part of the paper we provide a 4d origin for a gauge/LG duality already stated in the literature, that does not descend from any known s-confining duality. In the last part of the paper we focus on dualities for $\mathrm{SU}(n)$ and $\mathrm{USp}(2n)$ models with antisymmetric Fermi multiplets, obtained from dimensional reduction of 4d parent dualities.

By generalizing the construction of genuine multi-entropy ${\rm GM}[\mathtt{q}]$ for genuine multi-partite entanglement proposed in the previous paper arXiv:2504.01625, we give a prescription on how to construct ${\rm GM}[\mathtt{q}]$ systematically for any $\mathtt{q}$. The crucial point is that our construction naturally fits to the partition number $p(\mathtt{a})$ of integer $\mathtt{a}$. For general $\mathtt{q}$, ${\rm GM}[\mathtt{q}]$ contains $N (\mathtt{q}) = p(\mathtt{q})-p(\mathtt{q}-1)-1$ number of free parameters. Furthermore, these give $N (\mathtt{q})+1$ number of new diagnostics for genuine $\mathtt{q}$-partite entanglement. Especially for $\mathtt{q}=4$ case, this reproduces not only the known diagnostics pointed out by arXiv:1406.2663, but also a new diagnostics for quadripartite entanglement. We also study these ${\rm GM}[\mathtt{q}]$ for $\mathtt{q} = 4, 5$ in holography and show that these are of the order of ${\cal{O}}\left(1/G_N \right)$ both analytically and numerically. Our results give evidence that genuine multipartite entanglement is ubiquitous in holography. We discuss the connection to quantum error correction and the role of genuine multipartite entanglement in bulk reconstruction.

We propose a manifestly duality-invariant, Lorentz-invariant, and local action to describe quantum electrodynamics theory in the presence of magnetic monopoles that derives from Sen's formalism. By employing field strengths as the dynamical variables, rather than potentials, this formalism resolves longstanding ambiguities in prior frameworks. Our analysis finds consistent outcomes at both tree and loop levels using the established principles of quantum field theory, obviating the need for external assumptions or amendments. We clarify the mechanisms of charge renormalisation and demonstrate the renormalisation group invariance of the charge quantisation condition. Our approach can be useful for phenomenological studies and in quantum field theories with strong-weak dualities.

We analyse dynamics of the closed Type IIA and IIB string on various tri-vector deformed background searching for signatures of integrability. Using numerical methods we construct Poincar\'e sections for particular embeddings of the string and show that these are not destroyed under tri-vector deformation. We find that the corresponding Lyapunov exponents decay showing that trajectories do not diverge.

We construct a family of supersymmetric solutions in Type IIB supergravity of the form ${\rm WAdS}_3\times {\rm WS}^3\times T^4$, where ${\rm WAdS}_3$ and ${\rm WS^3}$ denote a warped anti-de Sitter spacetime and a warped 3-sphere, respectively, while $T^4$ denotes an internal 4-torus. These backgrounds are constructed by uplifting corresponding solutions in the $D=6$, $\mathcal{N}=(1,1)$ ungauged supergravity resulting from the compactification of Type IIB supergravity on a $T^4/\mathbb{Z}_2$-orientifold. More specifically, the supersymmetric solutions are ${\rm WAdS}_3\times {\rm WS}^3\times T^4$ with lightlike warped AdS$_3$ and ${\rm WAdS}_3\times {\rm S}^3\times T^4$ in which the warping of AdS$_3$ is generic. Moreover, we also construct solutions in the form of a warped product $\mathrm{LM}^3_{\zeta,\omega}\times_{{\rm w}} \mathrm{S}^3\times T^4$ of a 2-parameter deformation $\mathrm{LM}^3_{\zeta,\omega}$ of ${\rm AdS}_3$ and a three-sphere. We discuss the relation of these backgrounds to known solutions.

We investigate the $\phi^{2n}$ deformations of the O($N$)-symmetric (generalized) free theories with a flat boundary, where $n\geqslant 2$ is an integer. The generalized free theories refer to the $\Box^k$ free scalar theories with a higher-derivative kinetic term, which is related to the multicritical generalizations of the Lifshitz type. We assume that the (generalized) free theories and the deformed theories have boundary conformal symmetry and O($N$) global symmetry. The leading anomalous dimensions of some boundary operators are derived from the bulk multiplet recombination and analyticity constraints. We find that the $\epsilon^{1/2}$ expansion in the $\phi^6$-tricritical version of the special transition extends to other multicritical cases with larger odd integer $n$, and most of the higher derivative cases involve a noninteger power expansion in $\epsilon$. Using the analytic bootstrap, we further verify that the multiplet-recombination results are consistent with boundary crossing symmetry.

We have studied an $SO(4)$ gauged $O(5)$ Skyrmion on $\mathbb{R}^4$ which can be seen as a static soliton in $4+1$ dimension. This is a sequel of the known $SO(D)$ gauged $O(D+1)$ Skyrmions on $\mathbb{R}^D$ in $D=2$ and in $D=3$, with both of which its properties are compared. Two families of solutions are found, of these only one possessing a gauge decoupling limit. The curvatures of both of these solutions decay as $r^{-3}$, are bounded below by the topological charge, and are localised to an absolute scale. As such, they may have the potential of being interpreted as instantons.

Soft theorems describe the behavior of scattering amplitudes when one or several external particles are taken to be energetically soft. In tree-level gravity there are universal soft theorems for the three leading orders in the soft expansion, and they can be shown to be equivalent to Ward identities of asymptotic symmetries. While the leading and subleading symmetries are understood as supertranslations and superrotations respectively, the precise symmetry interpretation of the sub-subleading soft theorem is still a matter of investigation. The form of the sub-subleading soft graviton theorem was elucidated by Cachazo and Strominger using a BCFW expansion of graviton amplitudes. In this work we show that consistency with results based on asymptotic charges requires a careful treatment of collinear singularities in the amplitude, giving rise to collinear corrections to the usual Cachazo-Strominger soft theorem.

Let $X$ be a compact connected Riemann surface of genus $g \geq 3$ and $S \rightarrow X$ a $2:1$ branched covering defined by a generic quadratic differential on $X$. In the following notes, we explore how taking direct images of line bundles defined by certain distinguished special divisors on $S$ gives rank-2 bundles having nilpotent Higgs fields on $X$. The key ingredient is the notion of Baker-Akhiezer divisors associated to Higgs bundles and choices of subbundles of the underlying rank-2 bundles.

We study a point scalar charge in circular orbit around a topological star, a regular, horizonless soliton emerging from dimensional compactification of Einstein-Maxwell theory in five dimensions, which could describe qualitative properties of microstate geometries for astrophysical black holes. This is the first step towards studying extreme mass-ratio inspirals around these objects. We show that when the particle probes the spacetime close to the object, the scalar-wave flux deviates significantly from the corresponding black hole case. Furthermore, as the topological star approaches the black-hole limit, the inspiral can resonantly excite its long-lived modes, resulting in sharp features in the emitted flux. Although such resonances are too narrow to produce detectable dephasing, we estimate that a year-long inspiral down to the innermost stable circular orbit could accumulate a significant dephasing for most configurations relative to the black hole case. While a full parameter-estimation analysis is needed, the generically large deviations are likely to be within the sensitivity reach of future space-based gravitational-wave detectors.

We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum map is everywhere regular. Our results take root in the recently proposed notion of a confining function and are motivated by ghost-ridden systems, for whom we put forward the first geometric definition.

For $\mathbb Z_3$-orbifold limits of K3, we provide a counterpart to the extensive studies by Nikulin and others of the geometry and symmetries of classical Kummer surfaces. In particular, we determine the group of holomorphic symplectic automorphisms of $\mathbb Z_3$-orbifold limits of K3. We moreover track this group within two of the Mathieu groups, which involves a variation of Kondo's lattice techniques that Taormina and Wendland introduced earlier in their study of the symmetries of Kummer surfaces and the genesis of their symmetry surfing programme. Specifically, we realise the finite group of symplectic automorphisms of this class of K3 surfaces as a subgroup of the sporadic groups Mathieu 12 and Mathieu 24 in terms of permutations of 12, resp. 24 elements. As a proof of concept, we construct an embedding that yields the largest Mathieu group when the symmetry group of $\mathbb Z_3$-orbifold K3s is combined with all symmetries of Kummer surfaces.

This dissertation highlights the contributions I have made to the field of theoretical nuclear physics, specifically in high-energy Quantum Chromodynamics (QCD). High-energy QCD is a robust subject and my research is refined to the sub-field of small-$x$ spin physics; small-$x$ physics is characterized by high-energy and density collisions and is well-suited for the Color Glass Condensate (CGC) effective field theory. Small-$x$ spin physics takes the ultra-relativistic description of high-energy QCD and gives special attention to spin-dependent interactions suppressed by powers of the center-of-mass energy. My expertise lies in exploring the theory and phenomenology relating to the KPS-CTT small-$x$ helicity evolution equations, a rubric that allows one to make predictions of the quarks' and gluons' distributions of spin at small-$x$. These predictions are heavily influenced by the initial conditions of the evolution, and the initial conditions are determined through analyses of world polarized data. My contributions focus on Bayesian parameter analysis, numerical and analytical calculations to discretize and cross-check the evolution equations, and the incorporation of a new observable into the pool of analyzed data. The results of such work show that the net amount of spin from quarks and gluons in the small-$x$ regime is predicted to be negative and/or potentially small; an analysis of polarized deep-inelastic scattering (DIS) and semi-inclusive DIS (SIDIS) data resulted in a net small-$x$ spin prediction that can be large and negative, but new results with the inclusion of data for single-inclusive jet production in polarized proton-proton ($pp$) collisions now estimate that the net amount of parton spin at small $x$ is small, with 1-$\sigma$ uncertainty that spans zero.

In this work, we study a non-geometrical perturbation to the stealth field, which means the background remains invariant. The stealh is homogeneous in a universe whose source is dust and demand that perturbation unchanged density. As a regular procedure, we introduce a parameter $\lambda$ to perturb the scalar field equation and get an intriguing expression of the equation, similar to a series expansion in $\lambda$. From this procedure, we distinguish and approach to discriminate solutions, and the numerical solutions show that the most significant contribution to the solution comes from the linear term of $\lambda$.

Recent analysis of the DESI Collaboration challenges the $\Lambda$-Cold Dark Matter ($\Lambda$CDM) model, suggesting evidence for a dynamic dark energy. These results are obtained in the context of generic parameterizations of the dark energy equation of state (EoS), which better fit the data when they exhibit an unphysical phantom behavior in the past. In this paper, we briefly analyze how ambiguous this latter conclusion can be in light of the background degeneracy between EoS parameterizations and minimally coupled quintessence scenarios. We then investigate whether the current observational data can be accommodated with a non-phantom, thawing dark energy EoS, typical of a broad class of quintessence models. We show that the thawing behavior of this EoS outperforms the CPL parameterization and is statistically competitive with $\Lambda$CDM while predicting cosmic acceleration as a transient phenomenon. Such a dynamic behavior aligns with theoretical arguments from string theory and offers a way out of the trans-Planckian problem that challenges the ever-accelerated $\Lambda$CDM paradigm.

A relativistic self-gravitating equilibrium system with steady flow as well as spherical symmetry is discovered. The energy-momentum tensor contains the contribution of a current related to the flow and the metric tensor does an off-diagonal component to balance with the flow momentum. The presence of the off-diagonal component of the metric implies the radial motion of the reference frame, which gives rise to a problem how the relativistic effect is included in thermodynamic observables for such a general relativistic system. This problem is solved by taking an instantaneously rest frame in which geometric thermodynamic observables read as previously and giving them the special relativistic effect emerged from the inverse transformation to the original frame pointwise. The solution of the thermodynamic observables in accord with the laws of thermodynamics and the theory of relativity is presented. Finally the relativistic structure equations for the equilibrium are derived, from which the general relativistic Poisson equation as well as the heat conduction one are developed exactly.

Explicit example, where the Hawking temperature of a black hole horizon is compatible with the black hole's R\'enyi entropy thermodynamic description, is constructed. It is shown that for every static, spherically symmetric, vacuum black hole space-time, a corresponding black hole solution can be derived, where the Hawking temperature is identical with the R\'enyi temperature, i.e. the one obtained from the R\'enyi entropy of the black hole via the 1st law of thermodynamics. In order to have this Hawking-R\'enyi type thermodynamic property, the black holes must be surrounded by an anisotropic fluid in the form of a Kiselev metric, where the properties of the fluid are uniquely determined by the mass of the black hole, $M$, and the R\'enyi parameter, {\lambda}. In the simplest Schwarzschild scenario, the system is found to be thermodynamically unstable, and the 3rd law of thermodynamics seems to play the role of a cosmic censor via placing an upper bound on the black hole's mass, by which preventing the black hole from loosing its horizon(s).

In the context of Berglund-Huebsch mirror symmetry, we compute the eigenvalues of the Frobenius endomorphism acting on a p-adic version of Borisov's complex. As a result, we conjecture an explicit formula for the number of points of crepant resolutions of invertible Calabi-Yau orbifolds defined over a finite field.

In this note, we investigate the stability of the dark energy model from time crystals proposed in [1]. We emphasize two ingredients, the coupling of the scalar field to gravity, and the fact that these time crystals are on an expanding FRW background, which play a crucial role in the field's dynamics. The Hubble parameter, which contributes a drag term to the equations of motion, grows with time until the scale factor diverges. When taken into account, these factors also alleviate the stability concern of [2].

It is well-known that the momentum spectra of particles confined to finite spatial volumes deviate from the continuous spectra used for unconfined particles. In this article, we consider real scalar particles confined to finite volumes with periodic boundary conditions, such that the particles' spectra are discrete. We directly compute the density matrices describing the decay processes $\phi \to \varphi^2$ and $\phi \to \varphi\chi\nu$, and subsequently derive expressions for the decay probabilities both for confined and unconfined particles. The latter decay process is used as a rough toy model for a neutron decaying into a proton, an electron, and an anti-electron neutrino. We propose that finite volume effects can have an impact on the outcomes of experiments measuring the neutron lifetime. In addition, our findings at the toy model level suggest that taking into account possible initial correlations between neutrons and their daughter particles might be relevant as well.

From a purely geometric (kinematic) perspective, black holes in four dimensional spacetimes can have event horizons with arbitrary topologies. It is only when energy conditions are imposed that the horizon's shape is constrained to be spherical. Despite this, exploring exotic horizon topologies remains theoretically intriguing since it allows to unveil structural aspects of General Relativity and gain intuition on energy condition violations. In the axisymmetric case, besides the well-known spherical topology, only a toroidal topology is consistent with the symmetry. Complete solutions, describing the entire exterior region of such toroidal black holes without singularities, have not been reported yet. To the best of our knowledge, the construction we present here is the first explicit example of a toroidal black hole solution in four spacetime dimensions that is free of singularities in the external region.

A generalised form of time-translation-invariance permits to re-derive the known generic phenomenology of ageing, which arises in many-body systems after a quench from an initially disordered system to a temperature $T\leq T_c$, at or below the critical temperature $T_c$. Generalised time-translation-invariance is obtained, out of equilibrium, from a change of representation of the Lie algebra generators of the dynamical symmetries of scale-invariance and time-translation-invariance. Observable consequences include the algebraic form of the scaling functions for large arguments of the two-time auto-correlators and auto-responses, the equality of the auto-correlation and the auto-response exponents $\lambda_C=\lambda_R$, the cross-over scaling form for an initially magnetised critical system and the explanation of a novel finite-size scaling if the auto-correlator or auto-response converge for large arguments $y=t/s\gg 1$ to a plateau. For global two-time correlators, the time-dependence involving the initial critical slip exponent $\Theta$ is confirmed and is generalised to all temperatures below criticality and to the global two-time response function, and their finite-size scaling is derived as well. This also includes the time-dependence of the squared global order-parameter. The celebrate Janssen-Schaub-Schmittmann scaling relation with the auto-correlation exponent is thereby extended to all temperatures below the critical temperature. A simple criterion on the relevance of non-linear terms in the stochastic equation of motion is derived, taking the dimensionality of couplings into account. Its applicability in a wide class of models is confirmed, for temperatures $T\leq T_c$. Relevance to experiments is also discussed.

We explore novel topological responses and axion-like phenomena in three-dimensional insulating systems with spacetime-dependent mass terms encoding domain walls. Via a dimensional-reduction approach, we derive a new axion-electromagnetic coupling term involving three axion fields. This term yields a topological current in the bulk and, under specific conditions of the axions, real-space topological defects such as magnetic-like monopoles and hopfions. Moreover, once one the axions acquires a constant value, a nontrivial boundary theory realizes a (2+1)-dimensional analog of the Witten effect, which shows that point-like vortices on the gapped boundary of the system acquire half-integer electric charge. Our findings reveal rich topological structures emerging from multi-axion theories, suggesting new avenues in the study of topological phases and defects.