Papers

Precision predictions for high-energy experiments rely on accurately evaluating multi-loop, multi-scale Feynman integrals in dimensional regularisation. The method of differential equations is by now the standard tool for this task, but its full power is only realised when the system can be brought into an $\varepsilon$-factorised form. In this talk, we present an algorithmic framework that systematically constructs $\varepsilon$-factorised differential equations for arbitrary integral families, independent of their underlying geometry. We work in the setting of twisted cohomology and study the space of differential forms associated with a given family of Feynman integrals in the Baikov representation. Our approach consists of two steps. First, we introduce a particular ordering for the Laporta algorithm that orders Feynman integrals within a sector according to their geometric properties. We observe that this order relation yields a basis whose differential equation is in a Laurent polynomial form in the dimensional regulator $\varepsilon$. In the second step, we systematically construct transformation matrices such that the resulting system is in the $\varepsilon$-factorised form.

We consider the low-energy effective action of the heterotic string and derive an analytic solution describing the first-order $\alpha'$ corrections to the supersymmetric and extremal BMPV black hole with three unequal charges. The solution interpolates between an asymptotically-flat region and the near-horizon geometry. We compute the corrected black hole entropy using a generalization of Wald formula available in the literature, which correctly accounts for the Lorentz Chern-Simons term. The resulting expression agrees with recent results in the literature, which are based on the evaluation of an appropriate supersymmetric index.

Analogously to the suppression of inflaton decays into conformally-coupled scalar fields in the original Starobinsky $R + R^2$ model of inflation, inflaton decays to Standard Model fields are also suppressed in minimal no-scale models of inflation with field space curvature $\mathcal{R} = 2/3$. We study how this suppression can be avoided in generalized no-scale inflationary models. These include models in which the field space curvature $\mathcal{R} = 2/(3\alpha)$ with $\alpha \ne 1$ as exemplified by models derived from string theory, as well as models with non-minimal gauge kinetic terms and anomaly-induced couplings. We analyze direct and anomaly-induced inflaton couplings to gauge bosons and gauginos and demonstrate the Kähler-frame invariance of the physical gauge coupling. We determine the resulting reheating temperatures and the corresponding predictions in the $(n_s,r)$ plane. Finally, we consider an $R^3$ deformation of Starobinsky supergravity, which modifies the inflaton and stabilizer sectors but does not, by itself, generate new tree-level inflaton couplings to visible matter fields.

The convergence radius of Nekrasov partition functions (as a function of instanton counting parameters) is shown to be positive for 4d $\mathcal{N}=2$ quiver gauge theories with unitary gauge groups in an open dense subset of parameters. For $U(N)$ SQCD this is established if the ratio of equivariant parameters $b^2=\epsilon_1/\epsilon_2$ belongs to $\mathbb{C}\setminus[0,+\infty)$ and Coulomb parameters or masses are away from a lattice of hyperplanes. For general quivers it is only established for $b^2\in\mathbb{C}\setminus\mathbb{R}$. When gauge multiplets are asymptotically free, the radius is infinite, whereas in the (mass-deformed) conformal case the radius admits a positive lower bound that only depends on $b^2$. The proof relies on the expression of the partition function as a sum over tuples of partitions, and a proof of absolute convergence based on combinatorial inequalities on products of (co)hook lengths. Through the AGT correspondence this implies that large classes of Virasoro and W-algebra conformal blocks on the sphere or torus have positive convergence radius, for generic dimensions and complex central charges.

A class of time dependent backgrounds in two dimensional String Theory leads to superluminal Liouville walls on the worldsheet. In the dual double scaled $c=1$ matrix model these backgrounds involve eigenvalues leaking out to infinity, and the collective field fluctuations become strongly coupled along space-like regions, resembling singularities. We realize these backgrounds as results of quantum quenches in the matrix model, retaining non-linear terms in the matrix potential, thus departing from a double scaling limit. Working in the fermion picture in a Thomas-Fermi approximation, we show that while the early time behavior of the phase space density near the maximum of the potential agrees with that obtained in the double scaled theory, at times of the order $(\log N)$ the effect of the IR wall becomes significant. At later times, with a characteristic winding time of order $(\log N)^2$, folds on the fermi surface proliferate and eventually cover the allowed region in phase space densely. Using action-angle variables, we show that the phase space density oscillates around a time independent and angle independent value rapidly at late times. A coarse-grained density in the angle space relaxes to a time independent equilibrium value as a power law with an exponent largely independent of the details of the initial state. Thus, the appearance of a space-like singularity is an artifact of the strict double scaling limit. We comment on the interpretation of the final state in String Theory.

We study an exact static planar hairy black hole of Einstein gravity minimally coupled to a neutral scalar in four dimensions, which arises in a consistent truncation of type IIA supergravity on AdS$_4\times\mathbb{CP}^3$ dual to the ABJM theory. For nonzero hair the asymptotic region is hyperscaling violating rather than AdS, and the dual theory is a three-dimensional QFT deformed in the UV by an effectively marginally relevant operator with logarithmic running, which flows to the ABJM fixed point in the IR. On the gravity side, treating the hair parameter as an independent variable leads to a thermodynamic central charge $C_t$ and a generalized first law, organized by a radial scaling isometry. Holographic renormalization by the Hamilton–Jacobi method gives the one-point functions in closed form and the trace Ward identity. With the source held fixed, black branes exist below a maximal temperature $T_{\max}\simeq0.19\,\Lambda$ in two branches. On the stable branch the plasma approaches the conformal ABJM fluid with corrections of relative order $(T/\Lambda)^3$, which arise from a state-dependent rescaling of the boundary coordinates, while the other branch is governed by hyperscaling violation with $\theta=9$. A scale-invariant multi-trace boundary condition, which fixes the hair parameter instead of the source, selects the same solutions as the thermal states of a second theory, whose energy density is the bulk mass density and whose equilibrium thermodynamics is exactly conformal. Since the source mode is not normalizable, this second theory is established only in equilibrium, and the theory with fixed source is the dual of the solutions.

Particle cosmology is the branch of science that seeks to understand the birth and evolution of the Universe by applying the principles of particle physics. It brings together the physics of the very small (fundamental particles and forces) with the physics of the very large (the structure and evolution of the cosmos). In many ways, the early Universe acts as a natural laboratory - one far more energetic than any collider we can build - offering unique insights into phenomena that may never be accessible on Earth. Cosmological observations such as the Cosmic Microwave Background, the distribution of galaxies, and the accelerating expansion of the Universe serve as windows into the fundamental laws of nature. At the same time, theoretical developments in particle physics have led to theories, such as inflation, baryogenesis, and Dark Matter, that help explain key features of the cosmos.

We propose an algebraic framework for the strange metal regime of strongly correlated electrons. We show that the exceptional superconformal algebra $D(2,1;\alpha)$ admits two distinct contractions of its conformal sector: one to a pair of canonical fermions, the underlying degrees of freedom of the Landau–Fermi liquid (LFL), and one to the algebra of Hubbard operators, which characterise a distinct metallic regime, the Hubbard–Fermi liquid (HFL). We argue that competition between these two metallic states drives the emergence of the strange metal as a $0+1$D superconformal bath. We analyse the resulting thermodynamics, and at leading order obtain a parameter-free prediction, $4\pi^2\gamma^{-1} =\chi_s^{-1} + \chi_c^{-1}$, relating the Sommerfeld coefficient to the static spin and charge susceptibilities. We further show that the LFL-HFL transition is discontinuous at low temperature, forced by an algebraic constraint on the Hubbard contraction, and map out the resulting phase diagram. We connect the framework to microscopic lattice models and to the phenomenology of correlated insulators.

Following the holographic proposal that identifies the growth rate of Krylov complexity with the proper radial momentum of an infalling massive probe, we study Krylov complexity in Lifshitz and hyperscaling-violating backgrounds. For pure Lifshitz geometries, we find quadratic complexity growth for all values of the dynamical exponent. For hyperscaling-violating backgrounds, we show that the hyperscaling-violating exponent directly controls the late-time growth exponent, with a special limiting case exhibiting oscillatory behavior with a logarithmic envelope. We also extend our analysis to top-down string constructions, confirming the robustness of the scaling behaviors obtained in the bottom-up approach. Our analysis establishes that the momentum-Krylov correspondence extends naturally to non-relativistic holographic settings and remains well-defined despite the causal pathologies of Lifshitz spacetimes.

We propose that AdS$_3$ gravity coupled to dS$_2$ end-of-the-world branes is dual to a unitary holographic CFT$_2$ with non-unitary conformal boundary conditions. These boundary conditions have complex $g$-functions and appear in conjugate pairs. The associated gravitational path integral admits no real saddles, but does admit complex saddles. We show that an AdS$_3$ black hole microstate with a dS$_2$ brane behind the horizon corresponds to the unitary time evolution of a pure CFT state prepared by a Euclidean path integral on a cylinder with such boundary conditions. The construction predicts a boundary-condition-changing primary with $h=-c/8$, which resides in the boundary sector rather than the bulk spectrum and is therefore compatible with unitarity of the underlying CFT. This realizes dS holography as state preparation in a unitary AdS/CFT Hilbert space.

Exceptional points, where eigenvalues and eigenvectors coalesce, are a defining feature of non-Hermitian systems and have been extensively observed in photonic, atomic, and condensed matter systems. However, they have received little attention in quantum chromodynamics (QCD), which is the fundamental theory of quarks, gluons, and hadrons. We propose that imaginary magnetic fields provide a simple realization of non-Hermitian dynamics in hadronic systems. Based on two theoretical approaches, a hadronic effective Lagrangian and a constituent quark model, we compute mass spectra of neutral mesons and find exceptional points separating the real-spectrum and complex-eigenvalue regimes. In small fields, the real spectrum exhibits level attraction between hadronic states, whereas in larger fields, hadrons are deconfined, which is a signature of a field-induced inverted potential. Our findings open a new avenue for studying QCD dynamics in non-Hermitian environments.

Kaluza-Klein (KK) Gravitons are the direct collider imprints of the higher dimensional bulk physics in our four dimensional universe, arising from the compactification of an extra spatial dimension. In this work, we consider a two-brane warped geometry with a 5D $f(\mathcal R) = \mathcal R + \alpha\mathcal R^2$ gravity along with cosmological constant $\Lambda$. The warped spacetime provides an elegant resolution of the gauge-hierarchy problem without introducing any intermediate scale, while the Planck-scale curvature of the underlying $AdS_5$ bulk naturally motivates the inclusion of higher-curvature corrections. For small values of higher-curvature parameter ($\alpha$), we obtain the leading-order back-reacted warp factors perturbatively from the modified gravitational field equations. In the backdrop of a warped braneworld model, we have solved the Schrödinger-like equation governing the graviton fluctuations using a Euclidean path integral formalism, yielding the KK graviton spectrum and normalized wavefunctions directly from the corresponding quantum-mechanical propagator. Treating these results as the unperturbed background, we analytically determine the higher curvature corrections to KK graviton spectrum and their couplings to Standard Model (SM) matter fields. We find that there is an appreciable upward shift in the KK graviton masses while leaving the graviton-SM couplings only mildly modified as compared to a model with only Einstein gravity in the bulk. However the net cross-section of processes involving virtual gravitons appears to be suppressed whereas the dilepton and diphoton decay widths of the gravitons are significantly enhanced because of the higher curvature corrections. Overall, these effects lead to observable modifications to both the production and decay signatures of massive KK gravitons and may be probed in some future precision collider experiments.

We investigate the dynamical role of internal vibrational modes in the Abelian Higgs model, focusing on how Derrick-type excitations modify vortex dynamics and scattering processes. We study the scattering of excited vortices and show that the interplay between spectral flow and mode excitation generates effective forces and enables resonant energy transfer between translational and internal degrees of freedom. As a result, vortex dynamics become strongly non-adiabatic, exhibiting super-elastic collisions, oscillatory dependence of the final state on initial conditions, and the emergence of fractal structures in scattering diagrams. Our results demonstrate that internal vibrational modes play a fundamental role in vortex interactions, going beyond the standard moduli space approximation and revealing a rich phenomenology driven by mode dynamics.

We consider a very general scale-invariant scalar-tensor theory of gravity and its flat cosmological solutions. We show that any stable configuration with non-degenerate gravitational dynamics carries a non-vanishing cosmological constant, unless the quartic self-coupling of the scalar field vanishes. Since this condition is not protected against radiative corrections, a residual cosmological constant is expected as a generic and robust prediction of this class of theories. This result suggests that dark energy may be a natural consequence of an early scale-invariant phase of the Universe.

We study the critical behavior of the Lin-Lunin-Maldacena (LLM) geometry in the case when a droplet in the LLM base space develops a cusp. This cusp is a generic feature of the density of complex eigenvalues in the dual complex matrix model (CMM) computing the correlation functions of huge 1/2-BPS operators in $\mathcal{N}=4$ SYM theory. It is also related to the criticality in CMM describing the pure $2D$ quantum gravity behavior. The supergravity dual – LLM metric in the vicinity of the tip of the cusp – acquires a universal $ISO(1,3)\times SO(5)$ symmetric form, with a naked singularity along a half-infinite line. Both massless and massive particles get trapped by this line singularity for almost any impact parameter. Generic trajectories ending on the singular line reach it in finite affine time, while the corresponding observer time diverges. An explicit analytic solution for a large class of massless trajectories together with the absence of stochastic behavior in the vicinity of the cusp hint on a certain integrability of the problem.

Single-field ultra-slow-roll (USR) inflation is among the most studied mechanisms for primordial black hole (PBH) formation. When a non-stationary inflection point close to CMB scales is present, these models predict a negative spectral running ($\alpha_s<0$), whose magnitude increases with the PBH mass. This is in tension with recent hints for positive running from Atacama Cosmology Telescope (ACT) Cosmic Microwave Background (CMB) data. However, inflationary parameters inferred from CMB data are sensitive to the assumed pre-recombination expansion history, which is precisely where new physics motivated by the Hubble tension should operate. Focusing on axion-like early dark energy (EDE) as a benchmark, we investigate the effect of such pre-recombination new physics on $\alpha_s$, and hence on the viability of USR PBH models, in light of state-of-the-art CMB data from Planck, ACT, and the South Pole Telescope, together with Baryon Acoustic Oscillation data from DESI DR2. Our analysis therefore provides an updated set of constraints on $\alpha_s$ and the running of the running $\beta_s$. For most dataset combinations, moving from $\Lambda$CDM to EDE increases the inferred $\alpha_s$: once the acoustic angular scale $\theta_s$ is fixed, EDE increases the diffusion-to-acoustic angular scale ratio $\theta_d/\theta_s$, and the shift in $\alpha_s$ compensates this extra damping by increasing small-scale power. In this sense, tension calls for tension: taking the Hubble tension seriously as an indication for new physics strengthens the challenges faced by USR PBH models. More broadly, our analysis stresses that inflationary model selection using CMB-inferred inflationary parameters such as $n_s$ and $\alpha_s$ may be premature, especially until the Hubble tension, and more generally the pre-recombination expansion history, is understood.

In this paper, we investigate thick brane worlds in $f(R)$ gravity supported by two-scalar-field. The two-scalar sector provides an analytical warped background with tunable energy-density splitting, allowing us to test whether a Bloch-type internal structure can generate long-lived tensor perturbations resonances in the physically admissible region. We impose the positivity of \(f_R\equiv df/dR\), the derivative of the gravitational Lagrangian with respect to the Ricci scalar, which plays the role of an effective gravitational coupling in \(f(R)\) gravity. This separates the smooth ghost-free branch from a singular branch where this effective coupling vanishes. In the ghost-free branch, neither the relative-probability spectrum nor the phase-shift transmission spectrum shows narrow real-axis resonant peaks. These real-axis diagnostics indicate that the internal brane structure alone does not produce long-lived tensor resonances in the ghost-free region. Sharp quasi-localization peaks appear only in the singular branch, where the vanishing effective coupling induces divergent structures in the tensor potential; these peaks should therefore be interpreted as singular-boundary signals rather than ghost-free resonances of the smooth brane background. We then characterize the ghost-free massive Kaluza-Klein modes in the complex-frequency plane. Using the Asymptotic Iteration Method where applicable and time-domain evolutions with a supersymmetric partner potential as a zero-mode filtering tool, we extract the fundamental quasinormal frequencies. The modes have negative imaginary parts and quality factors \(Q\simeq0.9-1.9\), showing that the ghost-free massive tensor excitations are broad, short-lived dissipative modes. Thus the QNM spectrum provides the appropriate complex-frequency description of the Kaluza-Klein dynamics when no narrow real-axis resonances are resolved.

This thesis develops a kinetic-theory framework for relativistic dissipative magnetohydrodynamics under strong electromagnetic fields, motivated by quark-gluon plasma in heavy-ion collisions. Starting from the relativistic Boltzmann-Vlasov equation and using the method of moments within the 14-moment approximation, it derives causal second-order hydrodynamic equations for relativistic plasmas with increasing generality. The work first review relativistic dissipative hydrodynamics and its kinetic foundations, emphasizing the need for Israel-Stewart-type transient theories to preserve causality and stability. Electromagnetic fields are then introduced at the microscopic level, where the Lorentz force modifies the moment hierarchy and produces anisotropic transport effects absent in field-free fluids. Next, it develops relativistic dissipative magnetohydrodynamics for a non-resistive two-component plasma of oppositely charged particles. Here, the magnetic field couples the dissipative sectors of the two species, generating relative dissipative currents and coupled shear dynamics. For Bjorken expansion, the theory predicts damped oscillations in the transverse shear sector associated with cyclotron motion. Finally, the thesis treats the resistive two-component case, where the electric field evolves dynamically and couples to charge diffusion and shear stress. The resulting theory reveals current-shear feedback, transient electromagnetic generation of momentum anisotropy, and underdamped dissipative oscillations. Applications to homogeneous and Bjorken-expanding plasmas show how resistive and electromagnetic effects modify evolution beyond standard hydrodynamics. Overall, the thesis extends relativistic dissipative hydrodynamics to magnetized and resistive plasmas, providing a microscopic foundation for future studies of strongly magnetized quark-gluon plasma and astrophysical systems.

We consider classical 2d lattice models with face interactions defined in terms of a fusion category. The symmetries of such models typically include an algebra of topological operators sitting on a closed path in the lattice. In the case when the face interactions obey the Temperley-Lieb (TL) relations, we present a generic algorithm to determine the decomposition of the transfer-matrix space of states as a direct sum of simple TL modules. We apply this approach to several examples, and analyse the action of topological operators. As an application, we compute the modular transformation of the irreducible TL characters at primitive roots of unity.

In this work, we investigate the distance duality relation (DDR) in symmetric teleparallel theories, where gravity is mediated by nonmetricity. Starting from the general metric-affine formulation and adopting the geometrical optics approximation, we show that the standard Etherington reciprocity relation remains valid in the presence of nonmetricity when electromagnetism is minimally coupled and the photon number is conserved. We then extend the analysis to a class of $f(Q)$ theories with a nonminimal coupling between the electromagnetic field and the nonmetricity scalar. We demonstrate that such an interaction modifies the conservation of the photon number current, leading to a dynamical violation of the DDR. Focusing on a homogeneous and isotropic spacetime background in the coincident gauge, we derive a generalized DDR formula that directly relates observational distance measures to the Hubble expansion rate. Furthermore, we discuss the link between the deviations from Etherington's relation and variations of the effective fine-structure constant. Specific illustrative examples of the coupling function are also analyzed, showing that phenomenologically viable models predict only small deviations from the standard DDR. Our results provide a unified framework to distinguish between the geometric and dynamical origins of DDR violations, opening new avenues for testing non-Riemannian gravity with future high-precision astrophysical and cosmological observations.

We present a complete treatment of fifth-order renormalized galaxy bias at the one- and two-loop level in real space, including gradient corrections to deterministic bias operators at next-to-leading order. We then provide a complete computation of the two-loop power spectrum as well as the one-loop bispectrum and trispectrum of biased tracers, and demonstrate how to jointly model these statistics in a fully renormalized framework. These statistics also require stochastic renormalization of products of two, three or four operators at coincidence, which we include at leading order in gradients by means of an operator product expansion. We verify that all UV limits of loop integrals are absorbed by the counterterms we consider. Upon solving the resulting renormalization group equations, we find a pronounced scale-dependence of higher-gradient bias coefficients. Since our renormalization prescription is performed manifestly at the operator level, our results can also easily be extended to higher $N$-point functions, higher loop orders and field-level analyses.

We study a broad class of constrained mimetic-type extensions of general relativity with action $S=\int{\rm d}^4x\sqrt{-g}\,\bigl(R/2+\lambda\,C[g,\Psi]+{\cal L}_{\rm m}\bigr)$, where $R$ is the Ricci scalar, $\lambda$ is a Lagrange multiplier, $C[g,\Psi]$ is a scalar functional of the metric and generic field content $\Psi$ (possibly involving $\Psi$ and its covariant derivatives) and ${\cal L}_{\rm m}$ is the matter Lagrangian. The branch $\bar\lambda\to 0$, with the bar denoting a background value, provides a simple screening-like limit in which the constrained sector decouples, as in cosmological realizations where $\bar\lambda$ is typically nonzero on large scales while locally one expects $\bar\lambda\simeq 0$. On the exactly stealth branch $\bar{\lambda}=0$, the constrained sector drops out of the background dynamics, so, on domains where a background profile $\bar\Psi$ satisfying $\bar C=0$ exists, the theory admits the corresponding general relativity geometries as stealth solutions. As an explicit realization of this mechanism, we consider the scalar field case, where $C=g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi\pm1=0$ becomes a Hamilton-Jacobi equation selecting geodesic congruences; in this setting, we study spherically symmetric solutions and construct a stealth Kerr profile using Carter separability. We then show, at the general level, that the $\bar{\lambda}=0$ branch is perturbatively degenerate with general relativity: the constrained sector contributes to the dynamics only through terms weighted by $\bar\lambda$, which vanish on the stealth branch, while still imposing an infinite hierarchy of constraints on the fluctuations. Consequently, the $\bar\lambda\to0$ limit is generically non-uniform, making the would-be screening perturbatively pathological.

We study boundary conditions in GiMmsy's covariant and instantaneous formulations of classical field theories and show that the instantaneous state space in the presence of a constant Dirichlet boundary condition is a tangent bundle to the configuration space of fields satisfying said condition. We then study the instantaneous state space when only the velocity of the field is required to vanish at the boundary and show that this results in a sector structure, where each sector is a tangent bundle labeled by the configuration at the boundary. Taking the Legendre transform of this sectored state space yields a sectored phase space with leafwise canonical Poisson structures. We apply this to Yang-Mills theory with spatial boundary conditions and relate our results to flux superselection sectors. The sector-moving gauge transformations are not Hamiltonian because of the lack of a boundary momentum, prompting us to propose a novel definition of the asymptotic or boundary symmetry group as the quotient of the boundary-preserving Hamiltonian transformations by the trivial ones. The physical boundary symmetry group of electromagnetism is then shown to be a copy of the global gauge group even when all sectors are considered simultaneously. Conditions are discussed under which the same holds for non-Abelian Yang-Mills theory.

A family of heterotic compactifications carries more structure than a collection of solutions parametrised by moduli. Once the compactification data are fibred over moduli space, deformations become components of universal curvatures. This note reviews that organisation and explains how it incorporates the $\alpha'^2$ supersymmetry corrections.

We put forward a physical model of a relativistic Unruh-DeWitt battery moving along a general accelerated trajectory, including a linear motion and a circular motion with a reflecting boundary. The maximal amount of quantum work extraction, defined as the ergotropy, serves as a witness to Unruh effect modified by motion trajectories. It is found out that for a very low Unruh temperature, linear motion yields a high amount of ergotropy, while for a high temperature, circular motion becomes optimal for estimating the Unruh effect. For a specific acceleration, the ergotropy is the same for two different trajectories. The behavior demonstrates that, in a certain condition, one can simulate the work extraction of the accelerated battery in a linear motion by exploring the battery in circular motion. The observed ergotropy for the thermality is closely related to quantum coherence affected by spacetime vacuum fluctuations. In the presence of a reflecting boundary plane, we study different ways for the dynamics of the ergotropy. When the battery moves near the boundary, the prominent oscillation of the ergotropy will happen and exhibit some large instantaneous peaks. The interesting phenomenon results from the protection of quantum coherence for the accelerated battery in the vicinity of the boundary. Far away from the boundary, the oscillation behavior can be suppressed and the ergotropy rapidly arrives at a steady value. By contrast, the circular motion contributes to prolonging the oscillation evolution. The asymptotic amount of the ergotropy can rise progressively up to a saturation value with increasing the distance from the circular trajectory to the boundary plane. From the perspective of energy transfer, optimized quantum work extraction for the accelerated battery moving along a selected motion with a boundary plane is advantageous for probing Unruh thermality.

This paper explores the holographic Casimir effect associated with parallel spherical defects. The gravity dual is dominated by the AdS soliton with connected EOW branes at small widths, transitioning to AdS space with disconnected EOW branes as the width increases. Consequently, the holographic Casimir effect undergoes a first-order phase transition and vanishes in the disconnected phase. This new behavior highlights a significant difference from free theories, holographic parallel plane defects, and hyperbolic defects. Additionally, we confirm that the free theories adhere to the holographic bound for the Casimir effect in the case of parallel spherical defects. Interestingly, we observe that cosmic censorship provides a holographic interpretation of the attractive nature of the Casimir force when identical boundary conditions are imposed on both parallel surfaces. The repulsive Casimir force is associated with the bulk spacetime containing a naked singularity, which is generally considered forbidden. Additionally, we argue that topological censorship offers a natural explanation for why the vacuum of parallel defects is dual to the AdS soliton.

We review the notion of homotopy of quantum master actions in geometric Batalin-Vilkovisky formalism. Then we construct new examples of such homotopies, coming from renormalization group flow and non-infinitesimal changes of gauge fixing. Finally, we use the field redefinitions given by these homotopies to construct spans of quantum master actions with isomorphic effective actions.

In this paper, we investigate a fermion coupled to a Skyrme model in $2+1$ dimensions, where the Skyrmion is stabilized by the Dzyaloshinskii-Moriya and Skyrme interactions under a quadratic potential. This framework interpolates between the magnetic Skyrmion at the critical coupling and the baby-Skyrme limit. The Dirac equation is studied both analytically in a non-relativistic reduction and numerically for the full relativistic spectrum, and the parameter region admitting states bound to the Skyrmion is determined. Localized solutions exist only for electrically charged fermions with positive charge and negative angular momentum, and are absent for neutral fermions. The lowest bound state in each angular momentum sector is characterized as a function of the fermion mass, charge, and the coupling $h$ to the Skyrmion isospin, and its behavior is compared across the magnetic, baby, and mixed Skyrmion backgrounds. The resulting fermion–Skyrmion composite constitutes an electrically charged state bound to a topological texture, providing concrete signatures for potential future transport and scattering measurements in chiral magnets.

We investigate the geometrical, thermodynamic, and quantum emission properties of a rotating black hole immersed in a Hernquist dark matter halo. Starting from a static black hole spacetime surrounded by a Hernquist distribution, we construct its rotating counterpart through the noncomplexification formulation of the Newman-Janis algorithm and analyze the modifications induced by the independent halo parameters $\rho$ and $r_s$ and the rotation parameter $a$. The horizon structure is determined from the roots of the radial function $\Delta(r)$, while the stationary limit surfaces and the corresponding ergoregions are obtained from the condition $g_{tt}=0$. We show that the Hernquist contribution displaces the outer event horizon toward larger radii and modifies the size of the ergoregion, whereas rotation controls the oblateness of the horizon and the strength of frame dragging. We further derive the surface gravity, Hawking temperature, Bekenstein-Hawking entropy, and heat capacity. The quantum tunneling rate is obtained from the Hamilton-Jacobi method, leading to the corresponding occupation number and a thermal estimate of the particle creation density. Finally, we estimate the Hawking luminosity and evaporation timescales within a Stefan-Boltzmann approximation. All standard Kerr and Schwarzschild results are recovered in the appropriate limiting cases.

We revisit the calculation of the von Neumann (or "entanglement") entropy of a subsystem of a pure quantum state, under the assumption that the latter is drawn at random from a uniform distribution on the full Hilbert space. We derive simple and closed expressions for all power moments, from which the moments of the entropy can be computed by simple differentiation. Our approach (different from the usual one based on random matrix theory and Laguerre polynomials) makes use of Schur-Weyl duality and the character theory of the symmetric group $S_N$ . The paper is self-contained, providing all the necessary mathematical background.