Papers

We formulate a compact dynamical representation of quantum-information diagnostics for time-dependent two-mode bosonic systems in terms of the Bogoliubov ratio $\lambda_k(\eta)=\beta_k(\eta)/\alpha_k(\eta)$. For vacuum-evolved pure Gaussian pair states generated by a Hermitian quadratic Hamiltonian, $\lambda_k$ obeys a closed complex Riccati equation. After one partner mode is traced out, the reduced-state spectrum is determined by $q_k=|\lambda_k|^2$, from which the purity, linear entropy, Rényi-2 entropy, and von Neumann entropy follow directly. These Gaussian results are mathematically equivalent to those obtained from the standard density-matrix or covariance-matrix formalism; the advantage of the ratio representation is a compact separation between model-dependent dynamics and universal state diagnostics. Writing $\lambda_k=\sqrt{q_k}e^{i\theta_k}$ further exposes how pair production drives radial growth, whereas frequency rotation and detuning act through the phase and can suppress coherent squeezing accumulation. We also establish an exact extension to non-Gaussian $SU(1,1)$ sectors. For a lowest-weight Fock seed with conserved number difference $d$, the same ratio equation governs the evolution, while the reduced spectrum becomes a negative-binomial distribution determined by $(q_k,d)$. The Gaussian formulas are recovered at $d=0$. Cosmological perturbations and a chirped-pulse optical parametric amplifier illustrate the common dynamical mechanism and its information-theoretic consequences.

The origin of black hole entropy remains one of the deepest mysteries in modern physics. Two recent developments offer complementary perspectives on this puzzle: the entropy release from regular Schwarzschild black holes with a de Sitter core (the OCK construction), and the local thermodynamics of the de Sitter vacuum (Volovik). In the OCK framework, the inner horizon carries positive Bekenstein-Hawking entropy $S_{\rm inner}=\pi h_c^2$ that is gradually released as the core shrinks, until a classical Minkowski breaking obstructs the evolution at $n=0$. In Volovik's framework, the total entropy of a homogeneous de Sitter region is $S_{\rm dS}= \operatorname{sgn}(H)\,\pi/H^{2} = \operatorname{sgn}(H)\,A/4$: expanding de Sitter ($H>0$) carries positive entropy, while contracting de Sitter ($H<0$) carries negative entropy. We show that the sign of the Hubble parameter is the unifying element linking the two pictures. The OCK core is de~Sitter only for $n>2$; the Minkowski breaking is a classical kinematic obstruction, not a dynamical transition to a contracting de Sitter phase. Any connection between the expanding and contracting regimes would require a quantum mechanism that remains speculative. Nevertheless, both frameworks embody the same thermodynamic principle, the shrinking of the interior drives the system toward increased total entropy, and together they provide a consistent picture of entropy flow during gravitational collapse. The integer nature of the OCK parameter suggests a quantized entropy spectrum and a statistical interpretation of black hole entropy, while the generalized second law is satisfied in both frameworks, and in the speculated quantum connection provided the environmental entropy is properly accounted for.

Following previous results recently obtained by us, on Information Geometry versus Geometrical Thermodynamics and on the exact calculation of partition functions for extended Souriau Gibbs distributions on Calabi Vesentini manifolds, we study the differential geometry of the corresponding thermo-metrics. A general intriguing scheme is discovered and put into evidence. A small yet significant difference, distinguishes the even from the odd dimensional instance of the microscopic CV manifolds. Apart from that the complete thermo-space is flat when no constraint is introduced. Freezing the magnetic fields, which can be done according to complicated combinatorials, forces the thermo-system to evolve on curved submanifolds of the thermo–space that have a structure depending only on the length of the $n-1$ chain of frozen contiguous magnetic fields. The behavior of Riemann tensor components for such spaces is codified by a symmetric matrix with peculiar behavior along special symmetrically arranged submanifolds that, might be responsible for the generation of curvature walls and for the categorical partitioning of the thermo space. The embedding of this curved submanifold into $\mathbb{R}^{2n-1}$ can be traced back to the vanishing of magnetic fields and, in this case, the flat metric on $\mathbb{R}^{2n-1}$ is the $\mathfrak{a}_{2n-1}$ simple Lie algebra Cartan matrix. In another version the flat embedding reveals the geometric interpretation of the $n$-manifold as a generalized translation hypersurface. The boundary at infinity has a hypercube structure whose face central points and vertices appear, numerically, to be the end-points of all geodesics depending only on their angular slope at the start. This general feature is reminiscent of the causal structure at infinity of Lorentzian space-times and of Penrose diagrams.

We consider the interaction of dynamical quarks with the ensemble of oriented and nonoriented center vortices proposed to describe flux-tube formation between quark probes in pure Yang-Mills theory. The quark sector is described in terms of bosonized color currents. Within this fluid-like framework, the infrared vortex–monopole condensate restricts finite-energy configurations to be color neutral. Furthermore, neutral distributions of constituent color densities embedded in the condensate generate frustrated regions, providing a mechanism for their localization into finite-size configurations. The resulting picture is consistent with lattice evidence indicating that center vortices play a central role in shaping the hadron spectrum.

We show that retarded correlators in conformal field theories of scalar primary operators evaluated at finite temperature using $AdS/CFT$ scale anomalously at large light like momenta. The anomalous scaling depends on the curvature of the horizon. Setting the momenta equal to the frequency $\omega$, the retarded correlator for black holes with planar horizons scales as $\omega^{\frac{2}{d+2} (2\Delta - d) }$ as opposed to the scaling behaviour of $\omega^{2\Delta - d}$ expected by dimensional analysis at generic fixed momenta and large frequencies. $\Delta$ is the dimension of the primary and $d$, the number of space-time dimensions. For black holes with spherical and hyperbolic horizons when the frequency squared equals the Casimir along the horizon, the retarded correlator scales as $\omega^{\frac{2\Delta -d}{2} }$. We establish this using exact results in $d=2$, and a numerical analysis of the Heun equation for the $AdS_5$ planar black hole and finally using the WKB approximation in general $d$. The exact result for black holes with hyperbolic horizon as well as the analysis at large $d$ provides additional checks for the anomalous scaling behaviour. Finally we evaluate the anomalous scaling exponent for the stress tensor correlator in all its 3 channels.

Do two Hamiltonians related by a non-invertible transformation necessarily share the same finite-temperature phase diagram? For a cluster-model interpolation $H(s)$ and its Kennedy–Tasaki dual $\tilde H(s)$, the map is a partial isometry and equates only their all-plus-sector partition functions. In one dimension, thermal order is forbidden on both sides, leaving only the common zero-temperature transition at $s=\tfrac12$. In three dimensions, however, the inequivalence is exact already at $s=0$: the cluster model has an analytic paramagnetic free energy, whereas its dual $\mathbb Z_2$ gauge theory has a deconfinement transition at $T_c\approx1.31$. Quantum Monte Carlo shows that the mismatch occupies a finite window of the interpolation, marked by a self-dual frozen wedge on the cluster side and a deconfined dome on the gauge side; once both close the two phase diagrams agree again, coinciding over the entire remaining interval up to the shared trivial endpoint $s=1$.

We study a Schwarzschild-like black hole embedded in an exponential-sphere (ESM) dark matter halo, characterized by a halo mass $M_0$ and a scale radius $r_0$. We first show that the halo's effect on the marginally bound orbit (MBO) and innermost stable circular orbit (ISCO) is richer than a simple shift: the characteristic radii and energies vary non-monotonically with $r_0$, dipping below their Schwarzschild values before recovering, while the angular momenta decrease monotonically; as a function of $M_0$, the response can even reverse sign depending on how extended the halo is, with only the ISCO energy remaining monotonic throughout. We classify periodic orbits by the rational frequency ratio $q=\omega_\phi/\omega_r-1=w+v/z$ and find that $r_0$ and $M_0$ leave clearly distinguishable imprints on the orbit spectrum. Using the numerical kludge framework, we compute the corresponding extreme-mass-ratio-inspiral (EMRI) waveforms and show that varying $r_0$ produces a strong, monotonic effect enlarging the orbits, lengthening the radial period, and introducing a clear dephasing while comparable variations in $M_0$ leave the signal nearly unchanged unless $M_0$ becomes a sizable fraction of the black hole mass. Together, these results indicate that EMRI waveforms can, in principle, disentangle the total mass of a dark matter halo from its spatial extent, offering a strong-field probe of the dark matter distribution around supermassive black holes.

We combine the axiverse with a negative cosmological constant $\Lambda$, both originating from the string landscape, and apply an observation-time-weighted anthropic argument. Adopting a uniform prior on $\Lambda$ and a typical string-motivated axion decay constant comparable to the reduced Planck scale, this framework predicts a $\sim 40\%$ probability of observing $0.1 < \Omega_m < 0.9$, thereby naturally resolving the long-standing fine-tuning and coincidence problems of dark energy. Unlike many scalar-field dark energy models, the anthropic Lambda-axion universe (ALAverse) statistically disfavors slow-roll dynamics, as slow-roll requires fine-tuning of the initial field displacement. Moreover, the negative cosmological constant renders fast-roll scenarios anthropically unfavorable, since they typically yield only a very brief observational window with positive dark energy density. Having ruled out both extremes, the ALAverse characteristically predicts a moderate-roll dynamics. We derive a two-parameter parametrization in terms of $\delta_\Omega$ and $|\varepsilon_s|$ that covers ALAverse solutions as well as a broad class of canonical and phantom field models. Current observational data yield $\delta_\Omega = -0.0498 \pm 0.0186$, corresponding to a $2.7\sigma$ rejection of $\Lambda$CDM ($\delta_\Omega = 0$) and single-field thawing phantom models ($\delta_\Omega > 0$). The data also show a mild preference for the ALAverse over slow-roll quintessence, a trend that can be conclusively tested with future high-precision measurements of the Hubble diagram.

Bridging the sim-to-real gap is a central problem in robotics, and the prevailing approach is to build increasingly accurate simulators. Here, we propose another approach based on renormalization: using effective, resolution-dependent parameters to absorb details omitted by the simulator and reproduce real behavior. These parameters may differ from measured physical values because they compensate for what the simulator leaves out. We demonstrate this mechanism analytically for proportional–derivative (PD) control at finite simulation frequency, where proportional feedback changes the effective derivative gain and derivative feedback changes the effective inertia. We then interpret dynamic rope manipulation and underwater swimming through the same perspective. Finally, we present a practical procedure for choosing observables, identifying omitted physics, and determining effective parameters. Renormalization offers robotics a complementary path across the sim-to-real gap: effective parameters, real behavior.

We argue that R-twisting implies the Seiberg-Witten curves of 4d Argyres-Douglas theories could be combined with the R-twisted circle to form the mapping tori of torus knots, inspired by Milnor fibration theorem. Then 3d gauge theories labeled by mapping tori are generated, which in the IR capture 4d BPS spectrum and mutations. This construction addresses the boundary problem of the domain wall approach in \cite{Cecotti:2011iy}. These 3d theories show a supersymmetry enhancement, and are related to 3d rank zero theories.

This thesis reviews recent advances in calculating the sphaleron rate, with particular emphasis on electroweak baryogenesis. It also provides pedagogical introductions to sphaleron- and instanton-induced baryon-number violation, the vacuum structure of non-Abelian gauge theories, and other topological field configurations, and suggests "an zi" as a possible Chinese term for "sphaleron" (see p. 3). Broader implications of first-order phase transitions for collider searches and primordial black hole formation are also discussed.

Although parity-time (PT)-symmetric Hamiltonians are often associated with real energy spectra, PT symmetry is neither a sufficient nor a necessary condition for a real spectrum. More generally, real spectra are associated with the broader class of pseudo-Hermitian Hamiltonians, of which PT-symmetric Hamiltonians constitute a simple subclass. Here, we investigate the nonequilibrium dynamics of the imbalanced-pairing Kitaev model, a prototypical pseudo-Hermitian system, under a linearly time-dependent chemical potential. The dynamics are analyzed within the biorthogonal framework using the concept of dynamical quantum phase transitions (DQPTs). We show that, under a linear ramp protocol, DQPTs occur only when the post-ramp Hamiltonian possesses a real energy spectrum. For positive values of the non-Hermiticity parameter ($\gamma>0$), where the energy spectrum remains entirely real, a ramp crossing a single quantum critical point gives rise to a single family of critical times, analogous to the Hermitian case. Furthermore, for ramps crossing two critical or exceptional points, the critical sweep velocity above which DQPTs disappear decreases as the non-Hermiticity parameter is reduced and vanishes in the staggered-pairing limit, $\gamma=-1$.

Planck-scale signatures of quantum gravity may emerge semiclassically not only through modifications of spacetime geometry but also through the geometry of momentum space. In this work, we develop a $(2+1)$-dimensional framework in which a noncommutative algebra of spacetime localization operators reconstructs a locally anti-de Sitter momentum-space geometry in the classical limit. The resulting momentum-space curvature deforms the phase-space structure, modifies particle kinematics, and leads to a finite renormalization of the particle mass. Using an effective configuration-space action, we derive the corresponding stress-energy tensor that consistently sources the classical Einstein equations without modifying the gravitational dynamics. The resulting spacetime is a deformed BTZ black hole whose conserved mass, horizon radius, Hawking temperature, and Bekenstein-Hawking entropy acquire finite Planck-scale corrections. We further investigate Hawking radiation using the Hamilton-Jacobi tunneling formalism and show that the return time of an emitted massless particle receives two distinct contributions: a geometric correction induced by curved momentum space and a dynamical correction arising from Hawking backreaction. Remarkably, the null geodesic equations remain unchanged, indicating that the observable effects originate entirely from the deformation of the effective spacetime geometry rather than from modifications of particle trajectories. These results provide a concrete semiclassical mechanism through which quantum kinematics encoded in curved momentum space can generate observable gravitational phenomena without requiring a quantization of spacetime itself, thereby offering a phenomenological bridge between quantum geometry and black-hole physics.

The near horizon region of a non extremal black hole has a universal Rindler form, but the strict horizon limit is not an ordinary Lorentzian geometry. In the String Carroll expansion of this non extremal near horizon metric,the transverse angular directions form a base and the time-radial Rindler directions appear as a distinguished two-dimensional longitudinal sector fibered over this base. We study how this String Carroll expansion behaves for the Reissner-Nordström (RN) black hole as the extremal limit is approached, where the expected near horizon geometry is the Lorentzian $AdS_2 \times S^2$ throat. We show that while for the four-dimensional non extremal RN geometry, the String Carroll expansion correctly captures the near horizon Rindler region, it is not sufficient to recover the extremal $AdS_2 \times S^2$ throat. The reason is that the higher order terms, which are suppressed in the String Carroll expansion, become essential in the extremal limit. We show that in Eddington-Finkelstein coordinates, the required contribution appears at second order and restores the radial dependence needed for the $AdS_2$ geometry. The extremal $AdS_2 \times S^2$ throat is then obtained as the zero-temperature limit of the scaled throat geometry. In static coordinates, the temporal sector of the extremal throat geometry can be obtained from a second order near horizon expansion, but the radial sector cannot be obtained from any finite order truncation and requires contributions from all orders in the near horizon expansion.

We propose a quantum-information-theoretic perspective on the Weak Gravity Conjecture through the behavior of Krylov spread complexity. For a charged thermofield double state holographically dual to an AdS Reissner–Nordström black hole, we show that the extremal limit on the black-hole side is accompanied by an effective freezing of Krylov spreading. In this regime, the return amplitude becomes effectively a pure phase, and the dual quantum state ceases to spread nontrivially in Krylov space. We then incorporate charged matter and study the effect of Schwinger pair production in the near-horizon region. Within this semiclassical near-extremal analysis, the frozen behavior is lifted once the discharge channel is opened, and the dynamics become nontrivial again. This suggests that the Weak Gravity Conjecture may admit a complexity-based interpretation in terms of the absence of exact freezing in the presence of an available discharge channel. More broadly, our results point to a new connection between the swampland program, black-hole physics, and quantum information theory.

We use the non-linearly coupled Einstein-matter field equations to prove four theorems that bound from above the dimensionless force function ${\cal F}=4\pi r^2\cdot p(r)$ in spatially regular curved spacetimes of spherically symmetric self-gravitating matter configurations [here $p(r)$ is the radially-dependent pressure inside the spatially regular matter configurations]. In particular, for generic (not necessarily isotropic) matter configurations it is proved that: (i) ${\cal F}\leq 2$ for matter fields that satisfy the dominant energy condition, and (ii) ${\cal F}\leq 1$ for matter fields with a non-positive energy-momentum trace. In addition, for self-gravitating isotropic matter configurations we derive the stronger upper bounds: (iii) ${\cal F}\leq 1$ for matter fields that satisfy the dominant energy condition, and (iv) ${\cal F}\leq 1/2$ for matter fields with a non-positive energy-momentum trace. Our analytically derived results are in accord with the spirit of the maximum force conjecture in general relativity.

We investigate the nonlinear dynamics of a Hamiltonian system containing a ghost degree of freedom coupled to a canonical sector through nonlinear interactions. The model consists of one positive-energy and one negative-energy mode, augmented by quartic and sextic nonlinearities that regularize the large-amplitude behavior of the system. Unlike conventional ghost models, which typically exhibit runaway trajectories due to the indefinite nature of the kinetic energy, the present Hamiltonian possesses a confining nonlinear structure that renders the accessible energy surfaces compact for finite total energy. We derive the equations of motion and analyze the geometric properties of the Hamiltonian flow. Particular attention is devoted to the interplay between local ghost-induced instability and global nonlinear confinement. We show that the sextic contribution dominates the asymptotic dynamics and prevents escape to infinity despite the presence of a negative-energy sector. As a consequence, the model provides a controlled framework for studying bounded dynamics in ghost-coupled systems. The phase-space structure is investigated through numerical integration, Poincaré surfaces of section, and Lyapunov analysis. Depending on the interaction strength and nonlinear couplings, the system exhibits a transition from regular quasi-periodic motion to chaotic dynamics characterized by positive maximal Lyapunov exponents. Remarkably, chaotic trajectories remain confined within compact regions of phase space, yielding a realization of bounded chaotic motion in a ghost-containing Hamiltonian system. These results provide a concrete example of how nonlinear self-interactions can regularize ghost dynamics at the classical level and indicate a useful prototype for studying stability, confinement, and chaos in nonstandard Hamiltonian theories.

After decades without a fully self-consistent thermodynamic formulation, recent proposals for Lorentzian Taub-NUT spacetime have yielded several inequivalent descriptions, each satisfying its own first law and Smarr relation, leaving unresolved which formulation is physically preferred. In this Letter we introduce a two-horizon diagnostic whose sector temperatures are fixed by harmonic mean relations before the thermodynamic variables are chosen. For uncharged Taub-NUT, the sum sector closes with the mass and NUT charge, whereas, within the restricted homogeneous class examined here, the difference sector requires the thermodynamic secondary hair $J_n=mn$. This result supports a bi-hair thermodynamic organization of the NUT parameter through $N=n$ and $J_n=mn$. Furthermore, this two-horizon framework offers a new route toward addressing similar thermodynamic nonuniqueness in other two-horizon systems when the first law and Smarr relation alone do not identify a physically preferred formulation.

We compute the weak-coupling free energy density of pure four-dimensional $\mathcal{N}=2$ supersymmetric Yang-Mills (SYM) theory through second order in the 't Hooft coupling $\lambda$ at finite temperature using effective-field-theory methods. The contribution from the hard scale $T$ is obtained from massless three-loop vacuum diagrams in the full theory, and that from the electric scale $\sqrt{\lambda}\,T$ from a two-loop calculation in the dimensionally reduced three-dimensional effective theory. In contrast to $\mathcal{N}=4$ SYM, the theory is asymptotically free: the coupling-renormalization counterterm, together with the EFT unit-operator counterterm, cancels all $1/\epsilon$ poles. The remaining renormalization-scale dependence is fixed by the one-loop beta function. The expansion reproduces earlier results through order $\lambda^{3/2}$, and the order-$\lambda^2$ term is new.

We show that the inclusion of a dimension-six operator in the Higgs potential has a dramatic impact on the stability of oscillons in the $SU(2)$ bosonic sector of the Standard Model, extending their lifetime by orders of magnitude. This happens for the physical value of the ratio between the Higgs and W boson masses, $m_H/m_W=1.556$ and for the dimension-six operator $O_6 = (\Phi^\dagger \Phi)^3$ whose coupling constant is below the current upper bound.

We present DualityCert, a symbolic verifier for candidate Seiberg-duality claims in four-dimensional N=1 quiver gauge theories. The verifier evaluates 't Hooft anomaly matching, superpotential R-charge consistency, central-charge matching, and a bounded chiral-ring proxy. A claim that passes receives a consistency certificate, which states that no tested inconsistency was found, not that the duality is proven. We use the verifier as a repair environment for language-model agents, which receive a deliberately broken claim and must edit it until it certifies. On a preregistered benchmark of 145 broken claims, with the analysis fixed before the first confirmatory model call, verifier-gated retry improves final repair success over a single attempt by +8.3 percentage points (pp) on deepseek-chat and +7.1 pp on qwen-plus (Holm-adjusted p<0.002). Under an equal budget of eleven attempts, the stop-first strategy portfolio underperforms independent verifier-filtered resampling by 10.3 percentage points on deepseek-chat but outperforms it by 14.7 points on qwen-plus, reversing the ordering of the two tested verifier-exploitation policies across the two confirmatory models. On qwen-plus, category-level verifier feedback is worth +8.7 pp over content-free retry, and interpretable obligation identities alone are worth +6.4 pp over structurally identical masked feedback. Neither effect is detected on deepseek-chat. Separately, a preregistered MiniMax-M2.5 extension again finds an iteration gain and independent verifier-filtered resampling outperforming the strategy portfolio. Which policy is better thus differs between the two models, while every winning policy uses the same cheap certificate. The verifier, benchmark, protocol, and all per-attempt records are released.

We present an interactive web platform that unifies the construction Feynman ribbon diagrams (FRDs), the evaluation of higher-rank Chern–Simons knot invariants, and the identification of FRD-like knots at higher crossing numbers. These tree-structured diagrams naturally represent arborescent knots, which we refer to throughout as FRD-like knots. Within a single visual environment, users can construct an FRD as a tensor network, evaluate its associated Chern–Simons invariants, and use the resulting invariant data to distinguish and identify the corresponding knot. To our knowledge, this is the first platform to combine diagrammatic construction, tensor-network evaluation, invariant computation, and knot identification within a unified workflow.

We give an explicit shuffle algebra model for the loop-nilpotent cohomological Hall algebra (CoHA) of a tripled quiver with canonical cubic potential. As consequences, we (1) relate the loop-nilpotent CoHA to the quantized Coulomb branch algebra of the corresponding quiver gauge theory, (2) show that the loop-nilpotent CoHA is supercommutative after specialization at $\hbar=0$, (3) give generators for both the loop-nilpotent CoHA and the full preprojective CoHA, and (4) obtain an explicit characterization of the BPS Lie algebra of the full preprojective CoHA via certain degree and divisibility conditions. This gives a new formula for the Kac polynomials of the quiver in terms of the dimensions of certain vector spaces of polynomials. We also prove a conjecture on the spherical generation of the localized shuffle algebra and show that for ADE quivers, the loop-nilpotent CoHA is the positive half of Drinfeld-Gavarini dual of the Yangian.

We use Monte Carlo data for the three-dimensional Ising model at the critical temperature to predict an emergent radial geometry of the bulk using machine learning. Specifically, we employ a differentiable solver for a probe field on an asymptotically $\mathrm{AdS}_4$ background, trained to reproduce the measured momentum-space two-point functions of the boundary operators ($\sigma$ and $\epsilon$). We find that a single metric cannot simultaneously serve both operators. Fitting each channel separately improves its own residual by a factor of three to five, but degrades the other by up to two orders of magnitude. We quantify this tension between the two operators and show that it survives changes to the momentum window and the lattice size. Our results numerically demonstrate that the bulk geometry of a theory with an $\mathcal{O}(1)$ central charge, such as the 3D Ising model, is not captured by a single classical metric.

We study the two-parameter static type-I vacuum black hole recently obtained from an electromagnetic seed by a nonlinear solution-generating map. Its parameter $B$ changes dimensionless horizon geometry, yet the Komar mass variation at fixed asymptotic time is incompatible with the entropy variation. Using the Iyer–Wald, Barnich–Brandt, and Lee–Wald constructions, we derive the surface-charge one-form throughout the regular solution space and show that it has a nonzero curl. The same obstruction is measured by symplectic flux through the limiting Weyl boundary. A field-dependent normalization of the stationary Killing field supplies an integrating factor; the resulting energy $H=m/(1+B^2m^2)^{3/2}$ is uniquely selected by Schwarzschild mass normalization within this class. Homothetic scaling leaves the fixed-$G$ phase space two-dimensional because its tangent carries nonzero exact-symmetry charges. In Weyl coordinates, spatial infinity at finite mass is a closed surface of revolution. Its Brown–York canonical response reproduces the Lee–Wald flux pointwise. The semi-infinite annular source of the massless background emerges as a nonuniform limit of this surface. Finally, with $y=Bm$, the mechanics takes the global form $\text{d} M=T\text{d} S+\Psi_y\text{d} y$. Thus $B$ labels a genuine geometric deformation while its variation acts as external-source work in the Hamiltonian associated with fixed boundary time.

We investigated how a magnetic topological defect affects the vacuum polarization of a charged massive scalar field in a flat $(3+1)$-dimensional space-time. The defect was modeled as an impenetrable to matter field finite-thickness tube with magnetic flux inside. We implemented the most general form of the Robin boundary condition on the surface of the magnetic tube, which enables a fully general analysis of the problem. We have found that in flat spacetime, the total vacuum energy generated by a magnetic topological defect depends on the curvature $\xi$, except for special cases corresponding to the Dirichlet and Neumann boundary conditions. By contrast, when Robin's general boundary conditions are imposed, the induced vacuum energy acquires an explicit dependence on the curvature coupling $\xi$, which is significant even in flat space-time. A detailed study of the dependence of the effect on the boundary condition parameter has been carried out. The obtained results highlight the nontrivial role played by boundary conditions in vacuum polarization phenomena.

The cooling of neutrons stars, which are composed of ultra-high-density nuclear matter, strongly depends on the equation of state because the dominant cooling sources are neutrinos produced in their interiors. Here, we investigate the cooling properties of neutron stars, focusing on effective nucleon masses, whose impacts have been recently examined in supernova explosion and proto-neutron star cooling. The uncertainties of effective masses originate from the difference in the attractive interaction of scalar meson and the definition of the Dirac and Landau masses. At first, we employ so-called Walecka models that allow these two masses to be introduced within a unified framework and evaluate the resulting cooling curves. Based on the Walecka model, we compute the emissivity of the neutrons and the direct Urca process and their cooling curves. We demonstrate that the Dirac and Landau masses affect cooling of massive neutron stars, although most previous cooling simulations do not distinguish them. We also perform cooling simulations with two realistic equation of states based on relativistic mean-field (RMF) theory, whose differences arise from properties of only effective masses among characteristic parameters. These results are broadly consistent with those obtained from the Walecka models, indicating that the treatment of effective nucleon masses may be an important source of uncertainty in neutron-star cooling.

We investigate the viability of the light inflaton scenario in light of the latest inflationary constraints from the Atacama Cosmology Telescope (ACT), together with bounds from collider and intensity-frontier experiments searching for a feebly coupled light scalar with a sub-GeV mass. Assuming a quartic inflaton potential, we identify the region of parameter space consistent with the ACT observations and derive constraints on the inflaton mass and inflaton-Higgs mixing using results from NA62, KOTO, BaBar, Belle, LHCb, MATHUSLA, FASER2, SHiP, and neutral meson oscillations. We also explore the prospects for dark matter production during reheating within this framework, while remaining consistent with the inflationary observables.

Rotation serves as a pivotal control parameter for QCD matter, yet effective models and lattice QCD yield conflicting predictions regarding its effect on the deconfinement transition. Using a rotation-magnetic correspondence within a holographic framework, we investigate the rotational response of pure gluonic matter. Calibrated against lattice QCD data at imaginary angular velocity, we find real rotation enhances chromomagnetic string tension and raises deconfinement temperature, consistent with lattice QCD analytic-continuation predictions. The temperature dependence of chromomagnetic string tension dominates the system's Barnett response: weak low-temperature tension induces the negative Barnett effect, and slightly above the transition, spin contributions prevail to generate an anomalous negative total moment of inertia. Since growing angular velocity further strengthens chromomagnetic string tension and suppresses spin-dominated inversion, this anomalous regime only survives at weak real rotation and vanishes at large angular velocity. At high temperature, fully restored strong string tension stabilizes conventional Barnett behavior. Stemming from the melting and thermal restoration of nonperturbative chromomagnetic flux tubes, our results establish the chromomagnetic-induced inertia inversion (CII) mechanism as the microscopic origin of this anomalous rotational response.

I study a particular exact solution for static stars in four-dimensional non-projectable Horava gravity, which has been proposed as a renormalizable gravity model without the ghost problem by abandoning Einstein's equal-footing treatment of space and time through anisotropic scaling with z > 1. Considering the spherically symmetric static black-hole solutions in z = 3 Horava gravity as the exterior spacetimes of stars, I obtain an exact solution for incompressible (i.e., uniform-density) static stars with an arbitrary cosmological constant and isotropic pressure, and lambda=1, in which Birkhoff's theorem holds. For a vanishing cosmological constant, I obtain a modified Buchdahl bound on the maximum compactness for uniform-density stars, which ranges from 4/9 to 1. By contrast, I find that Ultra-Compact Objects (UCOs) with compactness C > 1 also exist with negative pressure while, surprisingly, satisfying all four standard energy conditions. UCOs include the regular (non-singular) black-hole solutions with masses above the extremal black-hole mass. In these solutions, the matter is localized at the timelike core region bounded by the inner horizon, while their exterior metrics are unaffected by the core matter and identical to the corresponding vacuum Horava black-hole solutions. These long-sought regular black-hole solutions are essential manifestations of Birkhoff's theorem in Horava gravity. I also find negative-mass stars with positive pressure that violate all standard energy conditions. Finally, I prove Buchdahl's theorem in non-projectable Horava gravity. The proof uses a weight-monotonicity condition on the average density and Birkhoff's theorem, together with the usual assumption that average density is non-increasing.