Papers

Five-dimensional 't Hooft-Polyakov monopole strings whose cores restore a non-abelian gauge symmetry become axion strings for extra-dimensional axions. The parametric separation between the string tension and the scale of quantum gravity admits a viable post-inflationary cosmology for high-quality axion dark matter.

We investigate the relation between Virasoro zero-mode evolution and the bulk logarithmic graviton in topologically massive gravity at the chiral point. By introducing additive coordinates adapted to the global time and radial dependence of the logarithmic mode, we obtain the expression \begin{equation} y(s,\bar s) = -s+\ln2 -\ln\!\left(1+e^{-(s+\bar s)}\right), \qquad s=\rho+i\tau, \quad \bar s=\rho-i\tau . \end{equation} This relation provides a direct bulk realization of the additive coordinates previously associated with the joint Virasoro zero-mode evolution. Near the AdS$_3$ boundary, the logarithmic coefficient becomes linear in $s$ up to an additive constant and exponentially suppressed corrections, while its exact finite-radius dependence is governed by the diagonal combination $s+\bar s=2\rho$. Upon complexification of the radial coordinate, this combination also organizes the periodic branch structure underlying the previously established bulk monodromy of the logarithmic graviton. The same diagonal coordinate controls the nilpotent part of the Virasoro zero-mode representation, providing a common additive-coordinate description of the representation-theoretic Jordan structure and the radial analytic structure of the bulk solution. The corresponding operations remain distinct: finite zero-mode evolution is algebraic, whereas bulk monodromy arises from analytic continuation and winding of the multivalued gravitational solution.

We investigate the bending of massless fields by a massive object in the presence of a curvature-scalar $\sqrt{-g}\xi R \phi^2$ non-minimal coupling up to one loop, using the perturbative quantum gravity computations. It is well known that without such coupling a self interacting scalar field theory cannot be renormalised in the presence of gravity. The massive object is modelled by a massive scalar $\phi$, and it is assumed to be non-relativistic, e.g., a star. We compute the 2-2 scattering of massless scalar and photons off this object via graviton exchanges. Assuming both $\xi$ and the bending angle to be small, we use the eikonal approximation to compute the angle up to ${\cal O}(\xi G^2)$. At tree level $({\cal O}(\xi G))$ we find no bending, and hence the ${\cal O}(\xi G^2)$ result happens to be leading in this case. The non-minimal vertices are qualitatively different from that of the standard minimal ones, e.g. $ \sqrt{G} h_{\mu\nu} T^{\mu\nu}$, as the former contains explicit momenta of the gravitons instead of the scalar, complementing the second. The bending angle is found to behave like $\sim b^{-7}$, where $b$ is the impact parameter. We have emphasised the qualitative differences of our results from that of the well studied minimal case.

The generalized unimodular theory is revisited and its consequence for cosmology is discussed. The usual matter components of the universe are obtained in a pure geometric way. This result gives a new perspective to the studies of the dark sector of the universe. A background and perturbative analysis are carried out, recovering the corresponding results obtained through the general relativity theory but with a different interpretation.

Considering two-fermion $F_a F_b$ productions and decays via one scalar or photon exchange at the $e^+e^-$ collider, we show that the rank $r_{\rho}$ of spin density matrix $\rho$ is equal to the number of degrees of freedom of the mediator. For one generic scalar exchange, the spin density matrix is rank one for a pure state. With rank-one condition, we can determine the spin analyzing powers for $F_a$ and $F_b$ and their product if the CP symmetry is violated and conserved, respectively, and probe the CP violation. These results can be applied to the $\eta_c \to \Lambda {\bar \Lambda}$ at the BESIII experiment and the Higgs $\to \tau \tau $ at the LHC. For one photon exchange, the spin density matrix is rank two for a mixed state. Considering the $\Lambda \bar \Lambda $ productions and decays at the BESIII experiment as an example, we show that the spin analyzing powers for $F_a$ and $ F_b$ can be determined by the rank-two conditions in details. Therefore, we can reconstruct the spin density matrices, probe the quantum entanglement and Bell non-locality, and evade the no-go theorem. Furthermore, we conjecture that the $N\times N$ spin density matrix with $r_{\rho} \le N-2 $ can be reconstructed at the lepton colliders in general.

We study the real-time linear response of gravitational waves in a time-dependent resonant scalar field in a Minkowski background. In the Schwinger-Keldysh formalism, we develop an adiabatic regularization scheme for unequal-time correlation functions and use it to extract the ultraviolet structure of the one-loop response. The leading divergence reproduces the familiar $\Box^2 h_{ij}$ structure, whereas the time-dependent background induces additional local divergences proportional to $\Box h_{ij}$, $\partial_0 h_{ij}$, and $h_{ij}$. These are renormalized by local counterterms associated with the Weyl-squared term, a time-dependent Ricci-scalar term, and a time-dependent cosmological constant. We also compare the renormalization of the linear response with that of the tadpole stress tensor and find a mismatch beyond leading adiabatic order in the present toy model. By considering a covariant completion of the resonance, we further argue that this mismatch is tied to the off-shell nature of the fixed background, and is expected to disappear once the background is treated on shell.

Adiabatically eliminating the quantum degrees of freedom in a mixed quantum-classical system produces an effective force in the classical equation of motion. The elimination can be made to any order in the adiabatic parameter, generating a series of higher order forces. By applying a sequence of near-identity unitary transformations to the quantum state, we derive a hierarchy of increasingly accurate effective actions for the classical variables. The third order Euler-Lagrange equation is non-Newtonian as the force depends on the jerk, the third order time derivative of position. We find that the third order terms induce a special kind of Kawaguchi geometry on the space of classical variables. This geometry is characterized by an almost symplectic structure and a differential line element that depends on the acceleration in addition to the velocity. Our results can be used to efficiently capture higher order nonadiabatic effects in molecular dynamics simulations.

False vacuum decay in scalar field theory is thought to be dominated by Coleman's O(4)-symmetric bounce, the minimum action nontrivial solution of the imaginary-time equations of motion. Beyond the bounce, non-constructive existence proofs of O(4)-breaking solutions are available in the mathematics literature, but the solutions themselves, and their physics, have remained unknown. Considering the simple, bounded-below, scalar field potential $V(\phi)=\frac{m^2}{2}\phi^2-\frac{\lambda}{4}\phi^4+\frac{g}{6}\phi^6$, we construct a nonradial solution explicitly: two bubble tubes of opposite sign wrapping orthogonal rings, invariant under ${\rm O}(2)\times{\rm O}(2)$ rotations combined with a $Z_2$ symmetry that exchanges the rings. The solution admits valid Cauchy data for real-time evolution from a $t=0$ slice, and supports an odd $>1$ number of unstable deformation modes. Having found this first solution we proceed to discover additional examples, in 3d as well as other 4d theories including a $Z_2$-violating potential and scalar QED for which there were no previously known existence proofs or O(4)-dominance theorems.

Four-dimensional gauge and gravitational theories exhibit long-range interactions that require asymptotic particles to be dressed by clouds of soft photons and gravitons. Faddeev-Kulish dressings render scattering amplitudes infrared-finite, but the resulting multi-particle states do not factorise into tensor products of dressed one-particle states. We show that this loss of Fock-space factorisation is not fundamental, but reflects an inappropriate choice of infrared variables. The real soft divergence is reproduced by the Goldstone modes of asymptotic symmetries, while the Coulomb phase is reproduced by new zero modes of the radiative fields that we introduce here. In these variables, infrared-finite dressed multi-particle states admit the usual Fock-space factorisation into single-particle dressed states.

Axiverse cosmic strings are resolved by non-perturbative string states with large tension. We show how, in some regions of moduli space, they dissolve into low-tension configurations that are fully captured by field-theoretic solitonic solutions, such as 't Hooft-Polyakov-like strings, allowing a post-inflationary cosmology within the original axiverse paradigm.

We develop a comprehensive, gauge-covariant geometric framework for non-Hermitian quantum systems in the quasi-Hermitian regime, that is, the region of parameter space where the non-Hermitian Hamiltonian admits a real spectrum and a positive-definite metric operator. We build this framework by elevating the Dyson map to a central geometric object. This map is the transformation that converts a non-Hermitian Hamiltonian into an equivalent Hermitian one. From it we construct the Dyson connection and decompose it into Hermitian and anti-Hermitian parts, identified respectively as stretching and rotation components. This decomposition cleanly separates the genuine physical metric deformations from the unitary gauge redundancies. Working with manifestly gauge-covariant states, we then derive the complex non-Hermitian Berry phase and the quantum geometric tensor (QGT), and show that the non-Hermitian geometric curvature originates from the non-commutativity of the stretching components at the operator level. We further analyse the geometric singularities near an exceptional point (EP) and uncover a distinct hierarchy of divergences. For a general two-level non-Hermitian model, the quantum metric tensor (QMT) exhibits a leading-order divergence $\sim |\epsilon_\mu|^{-2}$, while the Berry curvature shows a weaker, subleading divergence $\sim |\epsilon_\mu|^{-3/2}$, with $\epsilon_\mu$ denoting the parameter displacement from the EP along an individual parameter axis $\mu$. Finally, we examine physical realizations of this model, including the non-Hermitian Su–Schrieffer–Heeger (SSH) and Hatano–Nelson (HN) models, where exact analytical results confirm the predicted critical scaling laws and illustrate the metric-deformation-driven non-Hermitian geometries.

Multi-band gravitational-wave (GW) observation, combining space-borne and ground-based detectors across different frequency bands, can improve the sky localization of compact binary sources by two to three orders of magnitude compared to single-band detection. This enhancement is crucial for cross-correlation dark siren analyses, since the sky localization uncertainty directly determines the noise level of the GW angular power spectrum. In this work, we present the first Fisher forecast for cross-correlation dark siren cosmology with multi-band GW observations, cross-correlating GW events from the Einstein Telescope (ET), Cosmic Explorer (CE), and B-DECIGO with the Chinese Space-station Survey Telescope photometric galaxy survey. We compare three network configurations: the multi-band B-DECIGO+ET+2CE (BDET2CE), the ground-only ET+2CE (ET2CE), and B-DECIGO alone. In the $\Lambda$CDM model, BDET2CE achieves $\sigma(h)/h = 0.35\%$, improving by $37\%$ over the ground-only ET2CE ($0.55\%$) and by $86\%$ over B-DECIGO alone ($2.45\%$). Extending to the $w_0w_a$CDM framework, the multi-band advantage on cosmological parameters becomes more moderate, with BDET2CE improving $\sigma(h)/h$ by $\sim 4\%$ over ET2CE and $\sim 22\%$ over B-DECIGO. The most striking advantage of multi-band observation lies in the per-bin measurement of the GW clustering bias $b_{\rm GW}(z)$: at $z \sim 1-2$, BDET2CE constrains the bias to $\sim 3\%$ precision, compared to $\sim 8-60\%$ for ET2CE and $\sim 20-33\%$ for B-DECIGO. These precise, redshift-resolved bias measurements open a new avenue for probing the astrophysics of compact binary mergers, enabling constraints on formation channels such as isolated binary evolution and dynamical assembly that predict distinct clustering signatures.

We introduce a machine learning framework for extracting Ising topological order from defect partition functions of the two-dimensional Ising model on a torus. Restricted Boltzmann Machines (RBMs) are trained on Ising model data sampled at criticality across topological sectors. We take a component-wise square-root map of the learned distributions which naturally produces candidate wavefunctions for the (2+1)-dimensional Ising TQFT. As a nontrivial consistency check, we extract the modular S-matrix from overlaps of the resulting states and recover the expected Ising modular data. Our results demonstrate that neural network representations can capture both critical fluctuations and emergent topological structure, providing a data-driven route from lattice statistical mechanics to topological quantum field theory.

Some cumulants of the fluctuations of conserved charges soon above the chiral crossover behave as if the quarks were free. This was taken by many as evidence of deconfinement. At the same temperatures the mesonic correlators reveal the chiral spin and SU(4) symmetries, indicating that the propagating degrees of freedom are massless quarks connected into color singlets by the chromoelectric confining string. These correlators are qualitatively different from the free quark gas. Here we clarify the reason for the difference. The conserved quark number densities do not propagate in time but do propagate in spatial directions. The mesonic propagators calculated in full QCD differ radically from the free quark loop (quark gas) above T_ch. In contrast, the quark number density spatial propagator in full QCD at T > 220 MeV is very close to the free quark loop. In other words, the conserved charges do not see confinement, in contrast to the mesonic correlators. This is consistent with the well understood quark-hadron duality at T=0 in e^+e^- -> hadrons, where at invariant masses above 2 GeV the cross-section in the confining regime is represented by the free quark loop plus small perturbative corrections. All these features above T_ch but below the deconfinement temperature T_d can be combined within the following microscopic picture of the stringy fluid matter. It is a medium of the overlapping strongly interacting color singlet clusters. The quark interchanges between the clusters, required by Paili principle, make the quarks quasifree, which is reflected in fluctuations of conserved charges.

In this paper we present an integrable model in two dimensions. It is a deformation of the sine(sinh)-Gordon model. We give its Lax connection. We also obtain its (classical) $r$-matrix. It satisfies the classical Yang-Baxter equation. Thus, the model is a classical integrable field theory in two dimensions. The underlying algebra is a ${\cal Z}$-graded non-Lie alternative Akivis algebra. An alternative Akivis algebra is the tangent space at the identity of an analytic alternative loop as a Lie algebra is the tangent space at the identity of a Lie group. We expect the model to be integrable at the quantum level. We also give a family of classically integrable models which are related to the Poisson-Boltzmann equation in two dimensions.

We investigate the entanglement dynamics and Page curve of a 2D brane Maxwell-Scalar (MS) black hole coupled to thermal baths in double holography. Computing the entanglement entropy via the island formula, we find that injecting electric charge and scalar source into the system produce opposite effects: the former increases the degrees of freedom (DOF) on the brane by enhancing the effective global tension, thereby raising the saturation entropy of the system; conversely, the latter reduces the DOF on the brane by lowering the effective local tension near the IR geometry, ultimately suppressing the entanglement. Despite the non-trivial backreaction from the matter fields, the pre-saturation entanglement dynamics remain robust. We identify an early-time quadratic growth corresponding to the pre-local-thermalization phase, which smoothly transitions into a late-time linear growth. Furthermore, the scale of the Page time is governed by a competition between thermal excitations and the brane DOF. Higher temperatures accelerate the onset of the Page time by exciting more Hawking modes, while abundant DOF delay it by increasing the saturated entropy.

Random non-hermitian matrix ensembles with double-sided rotation invariance obey, in the limit of large matrix size, the Single Ring Theorem, which states that the support of the mean eigenvalue distribution in the complex plane is either a disk or an annulus. In contrast, rotational-invariant random normal matrix ensembles can have mean eigenvalue densities supported over any number of concentric annuli in the complex plane. In this paper we introduce and investigate, both analytically and numerically, a non-hermitian matrix model which flows from a generic matrix distribution obeying the Single Ring Theorem to a distribution of normal matrices by tuning a parameter which penalizes non-normality. We observe numerically breakdown of the Single Ring Theorem as the model flows towards normality, and determine the critical value of the parameter at which the transition occurs. We also study in detail the behavior of the singular values of these matrices under the flow. These singular values form a Fermi gas confined to the positive half-line. In particular, we find that at small values of the flow parameter, the interparticle spacings in the gas exhibit Wigner-Dyson repulsion, whereas for asymptotically large values of the flow parameter, at the normal matrix endpoint of the flow, the spacing statistics is Poissonian. The flow interpolates continuously between these two types of statistics. However, this change in statistics is not related directly to breaking of the Single Ring Theorem, which occurs very early-on along the flow, in the regime of Wigner-Dyson statistics. Finally, we introduce a certain ensemble of random permutations associated with the gas, and make a conjecture on how to use it in order to reconstruct approximately the average density of complex eigenvalues from that of the singular values in the large-$N$ limit.

We study flat gauging of continuous symmetries by summing over flat gauge-field configurations. We focus on the two-dimensional compact boson and construct the torus partition function with general flat $U(1)_M\times U(1)_W$ backgrounds. We show that flat gauging either $U(1)_M$ or $U(1)_W$ decompactifies the theory to the non-compact free boson, and that the dual $\mathbb{Z}$ background combines with the remaining $U(1)$ background into a non-compact $\mathbb{R}$ symmetry background due to the mixed anomaly. We also revisit the self-dual radius, where flat gauging the diagonal $SO(3)\subset (SU(2)_L\times SU(2)_R)/\mathbb{Z}_2$, first pointed out by Gaberdiel and Suchanek, gives the continuous orbifold which lies outside the usual $c=1$ moduli space. On the orbifold branch, we study finite and continuous non-invertible flat gaugings and explain why the continuous case requires a prescription for zero-measure fixed loci on the moduli space. Finally, we formulate the SymTFT of torus sigma models as a non-compact BF theory, whose topological boundary states encode the Narain moduli space and the $O(D,D;\mathbb{Z})$ T-duality action.

We investigate the observational appearance of a rotating black hole (BH) in Rastall gravity by analyzing its shadow and accretion signatures under different illumination environments. The spacetime geometry is characterized by the Rastall parameter $\mu$, the structure parameter $\gamma$, and the rotation parameter $a$. To visualize the BH environment, we employ a ray-tracing algorithm that follows photon trajectories from the observer's screen to the emission region. We analyze how the shadow radius, distortion, and photon ring morphology respond to changes in the spacetime parameters. For a fixed value of $a$, the shadow observables exhibit a pronounced dependence on the Rastall gravity parameters. In particular, increasing the structure parameter $\gamma$ leads to a gradual enlargement of the shadow radius, indicating an expansion of the photon capture region surrounding the BH. At the same time, the distortion parameter decreases, implying that the shadow boundary becomes progressively more circular and less deformed. These results suggest that larger values of $\gamma$ tend to suppress the asymmetry induced by rotation and enhance the apparent size of the shadow. Similar modifications are observed for different values of the Rastall parameter $\mu$, demonstrating that the combined effects of $\mu$ and $\gamma$ leave distinct signatures on the shadow morphology. Consequently, shadow observations may provide an effective tool for constraining the parameter space of rotating BHs in Rastall gravity.

In this paper we consider complex scalar field with Mexican hat potential coupled with Gauss-Bonnet scalar resulting in restored U(1) symmetry at the stage of inflation, corresponding to the modern cosmological horizon. In our model, the phase transition takes place during inflation, avoiding large-scale axion isocurvature perturbations. Our model provides strong primordial inhomogeneities on small scales and ultra-light axion-like particle as either a fuzzy dark matter candidate or a candidate for inhomogeneous dark energy. We also study the possibility of black hole formation and gravitational wave background in this scenario. We find that in the case when the symmetry breaking field does not backreact on inflation, black hole production is not feasible. However, under specific conditions, gravitational waves fitting the NANOGrav band can be obtained.

We study the evaporation and Page curve of charged near-AdS$_2$ black holes coupled to a non-gravitating bath at fixed temperature and chemical potential. The low-energy dynamics is governed by the Schwarzian reparametrization mode together with a $U(1)$ phase mode. We average the boundary energy and the outgoing flux over these two soft modes and obtain corrected balance equations for the temperature and chemical potential. We then use the corrected background to calculate the no-island and island entropies and the Page time shifts. We find that the two soft sectors affect the Page transition in our low-temperature semiclassical regime. The $U(1)$ phase mode correction delays the Page transition, while the Schwarzian correction tends to move it earlier. The total Page time shift is therefore determined by the competition between the Schwarzian and $U(1)$ sectors.

We derive thermodynamic currents for a perfect fluid of massive spin-1 particles obeying Bose-Einstein statistics within the Wigner-function approach. Using a covariant spin density matrix, we construct spin-extended equilibrium distributions and obtain the energy-momentum and spin tensors that match, up to second order in polarization, those of spin-1/2 systems and the Boltzmann case. We find that the approach yields a unified description of relativistic spin hydrodynamics independent of statistics and spin representation. Furthermore, the framework fulfills the requirements of the divergence-type theory, with nonlinearly causal and stable dynamical equations.

We investigate the emergence of generalized Schwarzian dynamics from a bulk-first BF perspective. Starting from two-dimensional BF gravity, we analyze the associated boundary phase space and its Drinfeld-Sokolov reductions. For the sl(2,R) theory, we recover the ordinary Schwarzian action as the reduced boundary dynamics arising from a particular sector of the BF asymptotic phase space. We then extend this construction to sl(3,R), where the reduced dynamics is governed by the second and third Wilczynski invariants, providing a natural higher-rank generalization of the Schwarzian derivative. In this framework, generalized Schwarzian dynamics emerges directly from flat BF connections and their companion forms rather than being introduced as an independent boundary theory. We further relate the resulting projective invariants to Casimir charges, monodromy data, and generalized Schwarzian thermodynamics, including monodromy spectra and semiclassical thermodynamics. In particular, constant projective invariants determine the corresponding Casimir sectors and monodromy data, which in turn organize the thermodynamic structure of the theory. Our results provide a unified bulk-first description of Schwarzian and generalized Schwarzian dynamics and reveal a direct link between BF gravity, asymptotic symmetry reductions, projective geometry, and boundary thermodynamics.

We further investigate the 3d gauged linear sigma model (GLSM)/~quantum K-theory correspondence for partial flag manifolds $X \equiv {\rm Fl}(\boldsymbol{k};n)$. This is a 3d uplift of the 2d GLSM/quantum cohomology correspondence with the 3d theory compactified on $\mathbb{R}^2\times S^1_\beta$. Recently, a set of half-BPS line operators, called Schubert line defects, were constructed that correspond to the Schubert classes in the K-theory ring of $X$. Utilizing algebro-geometric algorithms, we compute $2$-point and $3$-point correlation functions of these line operators in the 3d A-model regime of the theory. These are interpreted as genus-$0$ K-theoretic Gromov–Witten invariants, and they produce the K-theoretic Littlewood–Richardson coefficients of the quantum K-theory ring of $X$. We show how this works explicitly in examples, going beyond the existing results in the literature. Taking the small $\beta$ limit, we apply these techniques to the resulting 2d GLSM. We explicitly compute the quantum cohomology ring relations of $X$ for some cases and match with existing results in the literature in examples.

We study pseudo entropy $\mathcal{S}$, a recent generalization of entanglement entropy, for scalar cosmological perturbations in de Sitter space with sound speed $0.024 \leq c_s \leq 1$, and in expanding and contracting FLRW backgrounds with varying equation-of-state parameter $w$. In de Sitter space, $\mathrm{Re}(\mathcal{S})$ grows after horizon exit while $c_s$ controls its onset and saturates at late times. A similar saturation occurs in expanding-accelerating and contracting-decelerating backgrounds. In contrast, expanding-decelerating and contracting-accelerating backgrounds show large early-time $\mathrm{Re}(\mathcal{S})$ followed by oscillations after horizon re-entry. This happens because while the squeezing freezes, the squeezing angle doesn't. Unlike entanglement entropy, pseudo entropy possesses an imaginary part, $\mathrm{Im}(\mathcal{S})$, as well, which can encode the relative phase. $\mathrm{Im}(\mathcal{S})$ decays to zero in de Sitter and expanding-accelerating cases, but forms dense sub-Hubble oscillation bands in expanding-decelerating and contracting-accelerating backgrounds. Compared with entanglement entropy, Krylov complexity, and Nielsen circuit complexity, pseudo entropy captures otherwise hidden phase information; in the unsaturated regime, its slope is $\sqrt{2}$ times that of Nielsen complexity. Unlike circuit complexity, whose saturation bound is $w$-independent, pseudo entropy is sensitive to $w$ during the transition regime, making it a finer information theoretic diagnostic of cosmological dynamics.

We generalize the holographic entropy cone (HEC) to the holographic multi-entropy cone (HMEC) by adjoining multi-entropy coordinates to the standard bipartition entropy coordinates. We show that holographic states, through their multi-entropy vectors, form a rational polyhedral cone in multi-entropy space, and multicontraction maps provide exact certificates for holographic multi-entropy inequalities (HMEIs). We determine all facets of the $n=3,4$ HMECs, where $n$ includes the purifier, and obtain seven fundamental HMEI orbits: two for $n=3$ and five for $n=4$. We further propose two structural conjectures: HEC facet inequalities are convex combinations of HMEC facet inequalities, and HMEC facets obey a balanced-but-not-too-balanced principle.

In this paper, we would like to investigate the stability of de Sitter solution in the Einstein-Grisaru-Zanon gravity, which is a novel fourth-order gravity model considered recently in a paper [Phys. Lett. B 855 (2024) 138811]. As a result, we are able to derive the corresponding field equations for the Einstein-Grisaru-Zanon gravity by using an effective method based on the Euler-Lagrange equations. Unfortunately, one of the obtained field equations does not coincide with that derived in the original paper of the Einstein-Grisaru-Zanon gravity due to a gap between higher-order derivative terms. However, our de Sitter solution is still identical to one solved in the original paper of the Einstein-Grisaru-Zanon gravity due to the vanishing of the gap. Furthermore, a stability analysis based on the dynamical system method is performed to indicate that the obtained de Sitter solution is always unstable, no matter it presents an inflationary phase or expanding phase of universe. This result confirms the validity of stability investigation carried out in the original paper of the Einstein-Grisaru-Zanon gravity.

We revisit the variational principle for relativistic perfect fluids in a manifestly covariant formulation based on differential forms, with particular attention to the boundary data required for a well-posed action principle. For timelike flows, the formulation reproduces the standard formulation of Schutz and Brown. We then examine the extension obtained by replacing proper time normalization of the velocity with a nullity constraint, with the he Bi{\v c}ák-Kucha{\v r} null dust action emerging as a special case. Requiring the complete action to be invariant under local rescalings of the null flow vector imposes the condition that the energy density depend only on the entropy per particle. For this class of null flows, the conventional equilibrium condition, i.e., that the energy density is convex, fails at non-zero temperatures, therefore limiting the interpretation of the fluid as an ordinary thermodynamic system.

Motivated by Grand Unification, we study the formation of magnetic monopoles in an SU(3) non-Abelian gauge theory. We find that the number density of magnetic monopoles depends critically on a parameter, $\epsilon$, that controls the abundance and subsequent decay of biased domain walls. For sufficiently small but non-vanishing values of $\epsilon$, very few monopoles and walls survive in our simulations, potentially solving the cosmological monopole over-abundance problem. In addition, the scenario predicts a stochastic gravitational background from biased domain walls and the possibility of magnetically charged black holes.

The standard approach to perturbation theory for finite-temperature quantum field theories has several issues, including the appearance of ill-defined on-shell contributions in the real-time formulation, and infrared diverges in massless theories. Earlier studies indicate that these issues all stem from the inconsistent thermal generalisation of the Gell-Mann-Low relation, which forms the foundation of perturbation theory in vacuum. This inconsistency arises from the use of free scattering states in the relation, which are known not to exist in interacting thermal theories. In this work, we propose a generalisation of the Gell-Mann-Low relation for scalar theories based on non-perturbative spectral insights, namely that finite-temperature scattering states can be described by damped but stable particle-like excitations, so-called thermoparticles. The perturbative expansion of this generalised relation gives rise to contributions with exactly the same topology as the standard finite-temperature approach, except that now the propagators appearing in this expansion are not those of a free field but of thermoparticles, which depend on the dynamics of the theory. We demonstrate that thermoparticle perturbation theory resolves the known problems of the standard approach. Furthermore, by comparing imaginary-time calculations at two-loop level with numerical lattice simulations of two-point correlation functions in massive $\phi^{4}$ theory, we explicitly show that this framework gives rise to precise predictions, as in the vacuum case, in stark contrast to the standard approach.