Papers

We develop a comprehensive theoretical framework for Carrollian quantum mechanics by performing systematic ultra-relativistic contractions of the Klein–Gordon equation in the limit $c \to 0$. This limiting process uncovers three distinct sectors—time-like, space-like, and hybrid—each governed by a Carroll-invariant wave equation and accompanied by a consistent probabilistic interpretation. The time-like sector exhibits a novel temporal tunneling phenomenon, characterized by the relation $|\mathcal{T}|^2 = 1 + |\mathcal{R}|^2$, which reflects the indefinite character of the Klein–Gordon norm. In the space-like sector, the presence of spatial propagation necessitates a tachyonic dispersion relation, which forces the density to vanish for energy eigenstates, yielding zero-norm (null) states that gain physical relevance within Carrollian physics due to the underlying null geometric structure. The hybrid sector combines features of both sectors and admits two distinct formulations, which may be either tachyonic or non-tachyonic, and can be interpreted as an inhomogeneous Klein–Gordon equation. For all three sectors, we derive the corresponding continuity equations, probability densities, and currents, and investigate canonical quantum systems—including the particle in a box and tunneling phenomena—within the Carrollian regime.

We present an analysis of the perturbative modes of dissipation in the minimal warm inflation model where an axion-inflaton is coupled to a gluon thermal bath through the axion-gauge coupling. The corresponding friction coefficient, which generically is governed by IR physics, for the processes we consider is dominated by Landau damping of soft space-like gluons and the plasmon decay of hard on shell gluons. Since both of these processes are IR dominated, the friction coefficient becomes sensitive to the non-perturbative magnetic mass scale $m_{g}^{-1} \sim (\alpha T)^{-1}$ which in turn leads to the friction coefficient's overall linear proportionality to $\alpha$, which is much less suppressed in $\alpha$ powers compared to the well understood term from Chern-Simons (CS) diffusion $(\propto \alpha^5)$. On the other hand, this contribution to the friction coefficient is suppressed due to slow roll. We show that this can be viewed as a suppression of local spontaneous CPT violation for derivative couplings in general and that time correlations of nonlocal variables which do not fall off at large time separations are what allow an unsuppressed friction coefficient.

We investigate complex conformal field theories and interfaces between such theories, using methods of holography and two dimensional CFT. We use holography to prove the Im-flip property of complex conjugate CFTs. We construct a complex Janus solution and calculate some holographic observables. Complex RG-flow interfaces are obtained numerically. On the CFT side, complex interfaces are constructed for free boson CFTs with and without background charge. Boundary states are constructed, and transmission and reflection coefficients are calculated in both cases.

The chiral vortical effect (CVE) is the generation of an axial current in a rotating Weyl fermion; its description is presently based on semiclassical frameworks. In this work, we develop a fully quantum formulation for CVE, solving the exact evolution of microscopic spinful wavefunctions, which enables a bottom-up quantitative test of semi-classical theories and postulated distributions $f_{\text{CVE}}$ in different reference frames. Notably, it shows that $f_{\text{CVE}}$ is over a ground-state-free Floquet spectrum, qualitatively distinct from a thermal equilibrium distribution (i.e., fermi form $f_F$), underscoring CVE as a non-equilibrium phenomenon, distinguished from other chiral transports. The $f_F$ only approximately holds when three conditions are simultaneously fulfilled: (1) slow rotation $\omega R/v_F\ll 1$, (2) high chemical potential $\mu/(\hbar v_F R)\gg 1$, (3) isotropic symmetry, where $R$ is the size, $v_F$ is fermi velocity. In these conditions, the theory recovers established semiclassical results, including the current-response coefficients and the magnetization contribution; otherwise, it uncovers quantum phenomena such as “void states", deviation from the semiclassical formula $j_{\text{CVE}} \sim \mu^2$, a $v_F$-independent charge pumping. The theory is based on semimetals, providing more experimentally accessible detection than fundamental Weyl particles.

We construct a novel class of black bounce solutions within General Relativity, sourced by a canonical scalar field non-minimally coupled to linear electrodynamics, establishing a self-consistent framework in which regular black holes and traversable wormholes are supported by ordinary bulk matter, with the necessary exoticity confined to an infinitesimally thin defect at the bounce.

We study the out-of-equilibrium dynamics in the XX chain with step-like magnetic field, which maps to an inhomogeneous tight-binding chain after Jordan-Wigner transformation. We obtain exact analytic expressions for the fermionic two-point correlation function after a quantum quench from several initial product states, both homogeneous and inhomogeneous ones. This is achieved by using a combination of Fourier and Laplace transforms, which al low us to map the problem to a standard Riemann-Hilbert problem on the unit circle. For arbitrary positions and times the correlators are not expressed in terms of elementary functions. However, in the hydrodynamic limit $x,y,t\to\infty$ with fixed ratios, we provide explicit formulas that depend only on the effective transmission coefficient across the origin. We benchmark our analytic predictions against exact numerical simulations and find excellent agreement in the hydrodynamic limit, apart from finite-time corrections.

We consider a consistent deformation of the (anti)holomorphic generating system of [arXiv:2209.01966], aiming to provide a map to the (anti)holomorphic truncation of the Vasiliev theory. In our new formulation, the previously rigidly defined master-field $\Lambda$ can be shifted by $\mathrm{d}_z$-exact projective one-forms. The class of projective one-forms is described comprehensively, and corresponding projective identities are proven. $\mathrm{d}_z$-exact forms of the order $n$ in $C$ induce field redefinition of order $(n+1)$ and beyond. Explicit expression for the $(n+1)$-th order field redefinitions are provided. An analysis of the gauge transformation of the second order in $C$ in zero-forms is performed, identifying necessary and sufficient conditions for the part of the field redefinition of the second order that can be gauged away. The field redefinitions induced by the shift of $\Lambda$ are proven to be nontrivial.

We consider the properties of the gravitational radiation emitted by massive stars in binary systems with time varying mass, orbiting around each other in Keplerian orbits under the influence of the gravitational force. When this effect is combined to the quadrupole expression of the gravitational radiation, some supplementary terms in the standard formulae describing radiative effects do appear. By using the generalized quadrupole formalism, with time dependent masses, we obtain the expressions describing the time variation of the angular momentum, semimajor axis, eccentricity and periastron shift of the binary system. As a simple application of the developed formalism we consider in detail two cases of the mass variation, by assuming a linear and an exponential time dependence, respectively. The gravitational radiation characteristics corresponding to these models are fully investigated numerically with the help of a dedicated software package \href{https://github.com/croi900/GRAV-T}{GRAV-T}, specifically developed for the study of the gravitational radiation of the mass varying systems. The impact of the gravitational wave emission on the merger of two magnetars losing mass due to neutrino heated winds is also investigated in detail. The obtained results could be important for the understanding of general relativistic effects in the case of the variation of the gravitational mass with time, which sensitively influences the properties of the gravitational radiation emission.

By means of a higher-dimensional embedding approach, together with the study of distance, measure, and curvature, we construct a gravitational theory on the two-dimensional space over $p$-adic numbers. Before constructing this gravitational theory, we provide supplementary calculations based on existing literature and justify the validity of the gravitational theory by comparison with the real-number case, for instance, the curvatures of de Sitter(dS), anti-de Sitter(AdS), and Euclidean space should be positive, negative, and zero, respectively. Finally, as an example on the gravity side of the $p$-adic AdS$_2$/CFT$_1$, we present the action for a scalar field coupled to gravity.

Four-fermion interactions appear in effective descriptions of particle physics, many-body systems, and gravitational theories with fermions. Although the same local operator may enter perturbative scattering, a vacuum Nambu-Jona-Lasinio (NJL) instability, or finite-density Bardeen-Cooper-Schrieffer (BCS) pairing, these regimes are distinguished by their interaction channels, quadratic kernels, and quantum states. We give a pedagogical functional account of these distinctions and compute the local one-loop contribution of a scalar-channel NJL mean field to the energy-momentum tensor in curved spacetime. We first display the state data in the in-out functional and construct the closed-time-path functional required for an in-in expectation value. For the NJL saddle, a Hubbard-Stratonovich field shifts the fermion mass, and the parity-even Dirac determinant generates local volume, curvature, and curvature-squared operators. We find the covariant quantum effective action before specializing to a spatially flat FLRW background and derive the corresponding energy density and pressure. The constant-condensate limit agrees with the direct flat-space mean-field calculation. We also explain which additional state and channel data are required for finite-density BCS pairing and comment on renormalization conditions in curved spacetimes.

The general relativity may not be the final theory of gravity. One possible way to look for the gravity theory beyond general relativity is considering variable gravitational constant. Based on the quantum field theory, the gravitational constant as the coupling constant of gravity interaction may change along with the energy scale. Such scale dependent behavior of the gravitational constant can be well described by the functional renormalization group. In the current work, we investigate such behavior systematically. Firstly we find that such behavior is qualitatively independent of interactions such as the electromagnetic interaction included or not. But quantitatively the behavior is governed by two to-be-determined parameters. In general a limit scale may be introduced by the scale dependence of the gravitational constant. If we assume all physical scales are feasible, the two parameters are limited in some special regions. And more we compare the scale dependence behavior to the existing observations. We find the observation results constraint the two parameters strictly.

We analyze the possibility to construct propagators of flavor neutrinos, which are particles with indefinite masses. This kind of propagators was used previously while studying neutrino flavor oscillations in frames of the quantum field theory (QFT) based approach. Starting with the operator and the path integral formulations of the QFT, we obtain that the naive derivation of propagators for flavor neutrinos violates the basic principles of the QFT. Nevertheless, we can still construct the effective propagator of flavor neutrinos considering the mass mixing term as a perturbation. In this situation, the effective propagator arises from the solution of a Dyson-like equation. We use the derived effective propagator to rederive the quantum mechanical transition probability for neutrino oscillations in vacuum in frames of the QFT. The application of the obtained results to neutrino oscillations in background matter is also considered.

We compute the Casimir force between perfectly conducting parallel plates in a spacetime endowed with constant axial torsion. Working within an effective field theory framework where torsion couples to the electromagnetic sector via a gauge-invariant Chern–Simons-type interaction, we derive the modified photon dispersion relation and mode spectrum. Using zeta-function regularization, we obtain the vacuum energy and the resulting Casimir pressure to second order in the torsion parameter. Our calculation yields a correction scaling as $\Delta P/P_0 = -\frac{5\xi^2 S_z^2 a^2}{4\pi^2} + \order(S_z^4)$, which corresponds to a slight weakening of the attractive Casimir force. We acknowledge a known subtlety in the literature: because the Chern-Simons interaction is a total derivative, some analyses conclude that it should not contribute to the Casimir energy for standard boundary conditions, implying the leading correction is of higher order, $\order(S_z^4)$. For experimentally accessible plate separations ($a \sim \qty{1}{\micro\meter}$), the effect remains well below current detection thresholds ($|\Delta P/P_0| \lesssim 10^{-30}$) due to stringent bounds on macroscopic torsion from spin-torsion coupling experiments. Nevertheless, the calculation establishes a consistent, gauge-invariant bridge between quantum vacuum phenomena and non-Riemannian geometry. We discuss finite-temperature effects and geometric asymmetries as potential pathways for enhancing sensitivity, while placing the results in the broader context of dynamical torsion, condensed matter analogs, and quantum information protocols. Our results are consistent with the CPT-odd photon sector of the Standard-Model Extension and provide a geometric interpretation of Lorentz-violating coefficients in terms of spacetime torsion.

In Penrose's nonlinear graviton construction, a self-dual spacetime arises as the moduli space of holomorphic twistor lines in curved twistor space, whose explicit parametrization is concretely given by the incidence relation. We demonstrate a concrete local construction of the incidence relations for self-dual black hole spacetimes in Kerr-Schild coordinates: Eguchi-Hanson, self-dual Taub-NUT, and self-dual Plebański-Demiański. This is facilitated by implementing the Dunajski-Mason recursion in the framework of Plebański's second heavenly equation, for which we explicitly find the Plebański scalar. Our results describe closed-form formulae. Notably, for the self-dual Taub-NUT solution, the exact incidence relation exhibits linear dependence on the gravitational coupling. The construction of zero-rest-mass fields on self-dual black hole backgrounds is briefly sketched as an application.

We show that black hole horizons with non-constant curvature can be constructed in any even dimension, when the source of the Einstein equations is given by the stress-energy tensor of a non-linear sigma model of a particular class

Asymptotic states of massive particles in electrodynamics and gravity are not uniquely defined because of the absence of a mass gap. Working in the KMOC formalism, we study the classical implications of this freedom in the dressing of massive particle states. We show that coherent-state dressings modify observables by a large gauge/BMS transformation. The associated coherent-state displacement operator can be completed into a conserved charge, the BMS charge in the gravitational case, which implements large gauge transformations on scattering data. The parameter of our dressing is directly the large gauge/BMS transformation parameter, and we explain that observables do not depend on monopolar and dipolar parts of the transformation parameter to all orders. Our construction is driven by soft factorization rather than by an underlying local symmetry, and we illustrate this by exhibiting the same structure in a scalar theory with no gauge symmetry. We explore the action of large gauge transformations on two-particle states for scalar, abelian gauge and graviton mediators, obtaining a universal shift of the impact parameter and clarifying the frame dependence of the radiated angular momentum vis à vis the frame-independence of the total angular momentum. The transformation connecting the canonical BMS frame, in which the Schwarzschild metric takes the Kerr-Schild form, to the intrinsic frame, in which it takes the De Donder form, illustrates these effects concretely.

We discuss developments in the construction of Calabi–Yau manifolds by smoothing normal crossing unions of quasi-Fano manifolds, following the introduction of this method to the physics community in 2010. We describe constructions of Calabi–Yau threefolds with unbounded second Betti numbers and with very small Hodge numbers, as well as the first non-Kähler examples in dimensions greater than three. The role of Landau–Ginzburg models in mirror constructions is also explained.

Classical fractons are Hamiltonian systems that can develop attractors after projection onto configuration or shape variables, although the full phase space admits none. We study a scale-invariant, dipole-conserving two-parameter family of fracton Hamiltonians $H_{\alpha,\beta}$. By separating coordinates into scale and shape, we obtain autonomous shape dynamics that admit fixed points which leave a purely scale evolution of the form $R(t)\propto |t|^{\alpha/(\alpha-\beta)}$. The shape fixed points, which determine the distribution of the expanding particles, are central configurations of power-law Riesz potentials. The distinguished model $(\alpha,\beta)=(-2,1)$ is unique: its scale evolution takes the Einstein-de Sitter form $R(t)\propto |t|^{2/3}$, its fixed-point equation is the equal-mass Newtonian central-configuration, its large-$N$ distribution is a homogeneous ball, and its homothetic trajectories admit a zero-energy Newtonian gravitational dual. The fixed points are locally stable, and simulations at moderate $N$ approach them from random initial data. Large $N$ simulations reveal a richer class of fixed-points: bound clusters of approximately fixed physical size retain internal motion, while their centers approach unequal-mass Newtonian central configurations and preserve large-scale homogeneity. A scale-separation conjecture yields an effective unequal-mass fracton dynamics for the centers and a corresponding zero-energy Newtonian gravitational dual. Trajectories generically exhibit a bidirectional arrow of time: scale and shape complexity grow away from a Janus point, while Boltzmann entropy grows logarithmically. Together, these features reproduce the salient structure of a flat matter-dominated cosmology. In the distinguished fracton model, all these cosmological analogues emerge as attractor properties, making it a toy model for cosmological dynamics without fine-tuning.

We consider the recently found $\mathrm{AdS}_9$ backgrounds in type IIB supergravity. We start by reviewing the solutions in a more convenient set of coordinates, which allows us to explicitly compute a few relevant observables, including the holographic central charge. Subsequently, we study non-supersymmetric 7-brane configurations sourced by the IIB axio-dilaton. We find explicit analytic 7-brane solutions that possess the above $\mathrm{AdS}_9$ backgrounds as their near-horizon geometry. Finally, we discuss the relation of these 7-brane solutions to the R7 branes by imposing the reflection monodromy $\tau \rightarrow -\bar \tau$ in the transverse plane.

The AdS/CFT correspondence implies that the superconformal index ${\mathcal I}$ in ${\mathcal N=4}$ SU(N) supersymmetric Yang-Mills theory can be computed using the dual bulk theory. In particular, in the limit of large $N$, the index should be given by a sum over appropriate saddles. However, ${\mathcal I}$ depends on potentials $\sigma, \tau, \vec \Delta$ and, at large ${\rm Im}\, \tau = {\rm Im}\, \sigma$, the CFT index ${\mathcal I}$ rapidly approaches $1$ at all values of $N$. As a result, black hole saddles associated with exponentially large contributions in $N$ cannot contribute in this limit. This in particular excludes saddles that were previously suggested to be relevant in such regimes. We thus consider an approach to the bulk path integral motivated by taking it to be defined as an integral over real Lorentz-signature spacetimes with codimension-2 singularities. This approach leads only to saddles that satisfy the above bound, and to the enforcement of this bound via Stokes phenomena. We also find similar results for bulk AdS$_4$ calculations of the ABJM superconformal index.

In this work we aim to lay the foundation of flat version of AdS$_3$/BCFT$_2$ correspondence through Carrollian framework. We begin with discussing the recently discovered Boundary Carrollian Conformal Algebra (BCCA), the symmetry algebra of Carrollian BCFT. We identify this algebra at the null infinity of flat spacetime with appropriate choice of the end-of-the-world (EOW) brane. The properties of this EOW brane have been analysed both intrinsically and by taking flat limit from its AdS counterpart. We also find that the global as well as asymptotic symmetries of flat spacetime restricted by this EOW brane coincide exactly with the symmetries of BCCA.

Mesons and glueballs are paradigmatic bound states of confining quantum field theories (QFTs), but their nonperturbative spectroscopy in the continuum remains challenging beyond one spatial dimension. Here we perform such spectroscopy for the Ising QFT using a recently developed regularization based on noncommutative “fuzzy” geometry. On a thin fuzzy torus, we reproduce the universal low-lying $\mathbb E_8$ meson masses of the magnetically perturbed $(1{+}1)\mathrm{D}$ Ising QFT. By increasing the torus aspect ratio, we continuously track the second-lightest $\mathbb E_8$ meson as the system effectively crosses over from 1D to 2D. On the 2D fuzzy torus and sphere, we find a subthreshold scalar level and above-threshold response features consistent with previous estimates of glueball masses. The same excitations are revealed away from equilibrium using quench dynamics. Our results establish fuzzy geometries as nonperturbative spectroscopic probes of massive QFTs, including their bound-state evolution through dimensional crossover.

Magnetic monopoles are captured efficiently by neutron stars, and if they catalyze nucleon decay, the decay products would thermalize and generate observable X-ray surface emission. We use archival Chandra, XMM-Newton, and Swift-XRT data for old isolated millisecond pulsars to place conservative limits on the Galactic monopole flux ($F_M$). For a benchmark cross-section of $\sigma_{\Delta \rm B} \sim 10^{-27}\ {\rm cm^2}$, our constraint as a function of monopole mass $m_M$ is given by $F_{\rm M}(m_M) \lesssim 6 \times 10^{-19}~\mathrm{cm^{-2}s^{-1}sr^{-1}} \times \max \big(4 \times 10^{-6}, \min (2 \times 10^{11}~\mathrm{(GeV/c^2)}/m_{\rm M} , 1 ) \big)$. These limits improve previous neutron-star bounds, provide the strongest constraints to date on $F_M$ for $m_M$ between $10^{11} - 10^{13}\ {\rm GeV/c^2}$, and are competitive to existing constraints for this scenario. We also derive complementary constraints from the measured thermal emission of the Magnificent Seven. Our results demonstrate that neutron star X-ray observations provide a powerful probe of magnetic monopoles and motivate dedicated X-ray searches for old neutron stars as a means to test monopole-induced heating.

The length of the Einstein-Rosen bridge in sine-dilaton gravity at disk level equals the Krylov spread complexity of the dual double-scaled SYK (DSSYK) model, with the double-scaling parameter $\lambda$ controlling the semiclassical expansion. We compute the onset value, $L_{0}$, in the thermofield double state at $t=0$ and arbitrary inverse temperature $\beta$, through three loops and in closed form, extending the known one-loop result. The quantity $L_{0}$ represents the preparation complexity of the initial thermal Hartle-Hawking state. In DSSYK, $L_{0}$ is $\lambda$ times the average chord number of the thermal state, providing a microscopic, unambiguous determination of an additive constant otherwise fixed only by a choice of holographic renormalization scheme. The two-loop contribution follows from a saddle point evaluation of the DSSYK two-point function at coincident insertion points, where individually divergent contributions cancel only in their sum. At three loops, we bypass the saddle point analysis using an exact recursion relation that generates long high-temperature expansions at low cost, fixing and testing a proposed Ansatz against many independent data points. Finally, in the low-temperature regime each loop order contributes one further power of $\beta$, reorganizing the semiclassical series into an expansion in the Schwarzian coupling $\lambda\beta$, whose leading coefficient we check against an independent one-loop Schwarzian computation. The same methods, applied to the length variance and third-order cumulant at $t=0$, give their semiclassical expansion through two loops.

We give a Lefschetz thimble definition of the Chern–Simons–Kodama wavefunctional in Lorentzian self-dual gravity with positive cosmological constant. By complexifying the connection and choosing the Lefschetz thimble attached to the self-dual de~Sitter saddle, Witten's analytic continuation of Chern–Simons theory replaces the real contour, on which the defining integral is at best conditionally convergent, by an absolutely convergent integration cycle and yields a controlled semiclassical expansion. The relevant integrand is the full holomorphic exponential $e^{I}$, with $I=\kappa Y_{\rm CS}+(\text{source})$, and the steepest descent flow is governed by the Morse function $h=\operatorname{Re} I$. In the homogeneous isotropic de Sitter reduction, the construction reproduces the Hartle–Hawking Airy wavefunction. In the Bianchi~IX truncation, we take the Lefschetz thimble attached to the expanding de~Sitter saddle (the contracting branch defines a conjugate Lefschetz thimble); within this sector, the symmetric configuration is the only critical point for $\Lambda>0$. The corresponding Lefschetz thimble contains one trace direction with the FRW Airy structure and two anisotropic shear directions that are real-Gaussian damped at leading quadratic order. This gives a finite Bianchi~IX wavefunction which, to leading order, is the FRW Airy factor multiplied by a real anisotropy Gaussian. Thus, the Airy behavior is not an artifact of the one-dimensional minisuperspace reduction, but the leading form of the wavefunction on the Lefschetz thimble. We also discuss how the Lefschetz thimble prescription interfaces with Lorentzian reality conditions.

Neutrinos and other light relics leave characteristic imprints in the cosmic microwave background anisotropies, making their observation a sensitive probe of the particle content and thermal history of the early universe. The energy density in these relativistic species is parameterized by their effective number $N_\mathrm{eff}$. Measuring this parameter at the percent level, which is a long-standing science goal of CMB-S4 and other experiments, would test a wide range of well-motivated physics within and beyond the Standard Model of particle physics. In this paper, we present Fisher-matrix forecasts of the projected sensitivity to $N_\mathrm{eff}$ of several CMB-S4 survey configurations considered during its extensive design phase. The conceptual design reaches $\sigma(N_\mathrm{eff}) < 0.03$ over its seven-year observing period, while the revised configuration achieves the same precision over a longer timescale. We complement these results with a cosmic-variance-limited survey over the same multipole range to quantify the room for improvement accessible with additional instrumental, observational, and theoretical efforts. Finally, we discuss the broad implications of precise $N_\mathrm{eff}$ measurements for the radiation sector, big bang nucleosynthesis, light thermal relics, and other early-universe physics. The forecasts presented in this work are performed with the publicly released DRAFT (Dark Radiation Anisotropy Flowdown Team) tool. It provides an end-to-end pipeline from simulated foreground maps and component separation to delensing and projected sensitivities for any cosmological parameter, and it can be directly applied to other cosmic microwave background survey designs.

Spread complexity has emerged as a useful probe of quantum chaos, yet the microscopic spectral origin of its characteristic finite-time peak remains incompletely understood. We develop an analytic framework that relates spread complexity directly to local spectral statistics. Starting from an energy-space representation of the Krylov kernel, we show that the kernel is approximately banded, leading to a rapidly convergent diagonal expansion dominated by nearby levels in the ordered spectrum. Motivated by this structure, we propose an approximate kernel-universality hypothesis: after unfolding, the Krylov kernel is well approximated by that of a uniform lattice. Combining this universal kernel with local spectral statistics yields a simple analytic expression for spread complexity in terms of the Fourier transforms of the $k$-th nearest-neighbour spacing distributions. In particular, at leading order, the finite-time peak is controlled by the Fourier transform of the nearest-neighbour spacing distribution. The resulting framework describes both chaotic random-matrix ensembles and the integrable Poisson limit, identifies the spectral origin of the complexity peak and its late-time behaviour, and provides a direct connection between Krylov dynamics and spectral statistics.

We investigate a geometric approach referred to as the Conformal Killing Gravity (CKG), in which the dark energy sector emerges naturally from the conformal Killing symmetry of the Robertson–Walker space-time. Within this framework, the divergence-free conformal Killing tensor behaves as an effective perfect fluid, giving rise to a dynamical dark-energy component whose density, pressure, and equation of state are uniquely determined by the underlying geometry, without introducing any empirical dark-energy parametrization. The resulting CKG model extends the standard $\Lambda$CDM cosmology through a single additional parameter while recovering the $\Lambda$CDM limit in the absence of the geometric contribution. We constrain the model using Planck PR4 (NPIPE) CMB temperature, polarization, and lensing observations, ACT DR6 CMB lensing, DESI DR2 baryon acoustic oscillation measurements, and the Pantheon$+$, DES-Dovekie, and Union3 Type Ia supernova compilations. The analysis shows that the CKG favors a quintessence-like dark-energy evolution with no evidence for phantom crossing, while the reconstructed equation of state rapidly approaches the cosmological constant at earlier cosmic times. Furthermore, the model predicts a future critical redshift in the range $-0.8 \lesssim z_c \lesssim -0.7$, indicating that the present cosmic expansion eventually reaches a turning point before the formal singular limit at $z=-1$. Since the geometric contribution modifies only the post-recombination expansion history, the sound horizon remains essentially unchanged and the model does not provide a complete solution to the $H_0$ tension. Our results demonstrate that the CKG provides a simple, physically motivated, and observationally favored framework for describing the late-time accelerated expansion of the Universe.

The critical dynamics of a non-conserved order parameter is generally expected to become overdamped at long distances, even when propagating modes occur at microscopic or intermediate scales. We investigate the critical dynamics of a scalar field theory in thermal equilibrium which, in addition to local friction and noise, also contains a time-dependent second-order kinetic term. We show how to build a supersymmetric field-theory formulation. Using a two-loop expansion about four spatial dimensions, we show that the propagating and strictly overdamped limits share the same static Gaussian and Wilson-Fisher fixed points but realize distinct dynamical scaling regimes. The overdamped limit reproduces Model A. On the surface where local friction and noise vanish, the theory instead supports an interacting propagating fixed point whose dynamic exponent receives corrections at two loops. We demonstrate that coarse-graining does not generate a local dissipative operator on this surface, which therefore remains invariant under the RG flow. Local dissipation is nevertheless relevant at the propagating fixed point: an arbitrarily small equilibrium friction-noise perturbation drives the flow away from propagating scaling. Propagating critical dynamics thus defines a consistent but fine-tuned regime that is unstable to local equilibrium dissipation.

We consider the dynamics of a charged fermion in de Sitter space in the presence of a uniform background magnetic field, and discuss magnetic catalysis of chiral symmetry breaking using the Nambu–Jona-Lasinio (NJL) model. We evaluate the mode functions of the charged fermion field in this background by imposing the Bunch–Davies vacuum condition. The gap equation is solved in the mean-field approximation. We derive analytic expressions for the gap in several limiting regimes, such as the large-magnetic-field and large-curvature limits. We find that the curvature effect restores chiral symmetry, whereas the magnetic field enhances chiral symmetry breaking through the conventional mechanism of magnetic catalysis. The phase structure associated with chiral symmetry breaking is revealed by numerical calculations.