Papers

Cosmological lattice simulations have become important tools for studying non-perturbative dynamics in the early Universe. Many widely used codes, however, approximate the gravitational background by an exact Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime and neglect metric perturbations. We show that, during inflation, this approximation prevents the freezing of superhorizon modes. During slow roll, the curvature power spectrum decays as $H^4$, while the deviation becomes substantially stronger during ultra-slow roll. As a result, inflationary observables can be significantly distorted. In contrast, reheating studies appear to be considerably less sensitive to the omission of metric perturbations. We propose a practical criterion for assessing the validity of FLRW simulations based on the inclusion of first-order metric perturbations, and implement it in CosmoLattice.

We explore the properties of inner and outer horizon thermodynamics of dyonic Kerr-Sen black hole (DKSBH). It is observed that the entropy (or area) product is universal, depending only on the angular momentum of the BH. We then proceed to study the dual conformal field theory~(CFT) in the Kerr/CFT correspondence using thermodynamic relations and compute the central charges from 2D CFT. The central charges are found to be universal with only angular momentum dependence. By comparing to Kerr-Newman BH, it is found that the essential difference is in the right-moving sector of the CFT. Interestingly, we can then explicitly produce the non-vanishing central charges related to its static solution, the dyonic dilaton BH, using the thermodynamic method. Moreover, from the CFT relations to multi-horizon thermodynamics, we find the analytical expression of the quasi-normal modes~(QNM) spectra in terms of BH parameters. This QNM computation supports the Bekenstein-Hod conjecture on the BH's entropy quantization.

We investigate the effects of perturbative and non-perturbative quantum corrections on the thermodynamics of black holes immersed in a perfect fluid dark matter (PFDM) background with a cloud of strings (CoS) in asymptotically anti-de Sitter spacetime. Starting from the Bekenstein-Hawking entropy as the semiclassical baseline, we incorporate two distinct classes of corrections arising from small thermal fluctuations about thermodynamic equilibrium. In the perturbative sector, we derive the logarithmically corrected entropy and systematically compute the resulting modifications to the mass, Helmholtz free energy, Gibbs free energy, heat capacity, and pressure. The stability structure of the system is analyzed through the sign behavior of the heat capacity, which reveals a transition from a thermodynamically unstable to a stable phase. In the non-perturbative sector, we introduce exponential corrections to the entropy and carry out a parallel analysis of all thermodynamic quantities. We demonstrate that non-perturbative effects are negligible for large black holes but become significant as the horizon radius shrinks toward the Planck regime. In both sectors, we investigate the equation of state and search for a van der Waals-like critical point by examining the simultaneous vanishing of the first and second pressure derivatives with respect to thermodynamic volume; no such inflection point is found within the physically admissible domain. Our results illuminate the contrasting roles of logarithmic and exponential entropy corrections in governing the thermodynamic stability and phase structure of PFDM black holes with a CoS.

We introduce a basis for tree-level meromorphic scattering amplitudes suitable for describing pion scattering in the large-N limit. The basis is constructed as linear combinations of Lovelace-Shapiro-like amplitudes with varying Regge slopes and intercepts. The resulting amplitudes satisfy by construction the fundamental requirements of analyticity, crossing symmetry, and Regge behavior. We analyze their behavior in specific kinematical regimes, including the high-energy fixed-angle limit. We also show that finite linear combinations of our basis elements need not violate unitarity. Nonetheless, because unitarity is not imposed by construction, we enforce it a posteriori by requiring positivity of the partial-wave decomposition. This condition can be formulated as an optimization problem and solved numerically. The solutions to this primal bootstrap problem yield meromorphic amplitudes that satisfy all the aforementioned constraints. We compare several observables with the bounds obtained from the dual positivity conditions and show that our family of amplitudes spans the full allowed parameter space. With appropriate modifications, this method can be extended to construct amplitude families for broader applications.

We study the gauge-invariant dynamically conserved charges, and their corresponding densities, for instanton solutions of Yang-Mills theories in four dimensional Euclidean space, for the gauge group $SU(2)$. Those charges were constructed in [1,2] through the integral equations of Yang-Mills theory, using techniques on generalized loop spaces. We use the integral non-Abelian Gauss law to evaluate the gauge-invariant flux of the magnetic and electric non-Abelian fields through spherical surfaces centered at the origin of the instanton solution. From such a flux, we define gauge-invariant charge densities by considering the charge within an infinitesimal spherical shell of radius $r\equiv\sqrt{x_i \, x^i}/\lambda$, with $\lambda$ being the parameter of the instanton solution, defining its size, and $x_i \, x^i = (x^1)^2 + (x^{2})^2 + (x^{3})^2$. We discuss the issue of the reparameterization invariance of the charges and densities, and show that the magnetic and electric fluxes for the instanton and anti-instanton, at $r=1$ and $x^4 = 0$, $x^4$ being the Euclidean time, are non-zero and observable. Our results give an interesting picture of the internal structure of the instanton, and may be important for the properties of the Yang-Mills $\theta$-vacuum.

We investigate whether relativistic massless classical particles may emerge as the classical limit of massless quanta. To address this question independently of any specific dynamics, environment, or pointer basis, we develop an axiomatic and purely kinematical framework for the coarse-graining approach. In this formulation, a candidate classical phase space is taken as the outcome space of a POVM subject only to minimal classicality and covariance under the relevant spacetime symmetry group. Applying this framework to the Poincaré group, we prove a no-go theorem for massless particles: the covariance requirement is incompatible with the operational conditions for classicality. The theorem leaves open field-like limits of massless quanta, for example the emergence of electromagnetic or gravitational fields, while ruling out classical massless particles, such as classical photons or gravitons.

We study constraints on the quantum chromodynamics (QCD) axion in F-theory, a strongly coupled limit of string theory. We build models of QCD from compactifications to four dimensions on elliptic fibrations over toric threefolds $B_3$, characterized by an integer $N=h^{1,1}(B_3)$. The QCD axion mass increases with $N$, and we find that models with sufficiently high $N$ are inconsistent with observations of the neutrino burst from supernova 1987A, disfavoring large regions of the moduli space. Specifically, at least $95\%$ of models with $N \ge 8,791$ – a regime that arguably contains the vast majority of known F-theory topologies – have a QCD axion mass $m_{QCD}>15~meV$ and are thus constrained. This limit is independent of cosmology. We only consider weakly-curved threefolds, where $\alpha'$ corrections are plausibly negligible.

We demonstrate that all anti-self-dual Einstein metrics with non–zero cosmological constant $\Lambda$ locally arise from solutions of a single second order PDE introduced by Lipstein and Nagy. We show how this equation fits into the heavenly formalism of Plebański, and establish a Lax pair. Finally we show how Plebański's second heavenly equation arises in the limit as $\Lambda\rightarrow 0$.

We provide a complete proof that Yang–Baxter bi-vector deformations are solution generating transformations in Type II supergravity. The proof does not rely on the assumption that the vielbein is invariant under Lie derivative along all Killing vectors entering the bi-vector. We analyse transformation of boundary terms and derive a simple expression for the case, when the boundary does not change its geometrical locus.

We investigate the motion of spinning test particles in the spacetime of a global monopole in the framework of the Mathisson-Papapetrou-Dixon equations. By making use of the symmetries of the spacetime, we obtain a general exact solution to the equations of motion. We show that the particle's trajectories, momenta, and spin can be expressed in terms of three specific functions of the polar and azimuthal angles. We also show that the system is completely integrable. We obtain the general non-geodesic trajectory of the particle, and also examine the particular cases of radial and planar motion. We compare the non-geodesic trajectories of a spinning particle with a non-spinning particle.

We investigate the brane origin of supersymmetric and scale-separated AdS$_3$ flux vacua arising in a class of type IIB orientifold reductions with G$_2$-structure. First, using the effective three-dimensional supergravity together with explicit uplift formulae, we trace back the $F_{(7)}$ and $F_{(3)}$ fluxes responsible for scale separation and identify the type IIB background that is probed by the corresponding D1- and D5-branes. Second, by restoring such D1- and D5-branes, we obtain a type IIB solution that interpolates between the previous background in the asymptotic region and the scale-separated AdS$_3$ flux vacua in the near-horizon region. Third, by working directly in ten dimensions, we construct a codimension-one D1-D5-KK5 intersection whose near-horizon region realises the scale-separated AdS$_3$ flux vacua. Our results provide a higher-dimensional interpretation of these flux vacua in terms of (smeared) brane configurations.

A key challenge of gravitational-wave physics is distinguishing the nature of compact objects in binary coalescences, in particular whether they are black holes or neutron stars. Neutron stars are set apart by a stronger tidal response, whose static and dynamical aspects are directly linked to their rich internal physics. Measurements of this response through gravitational-wave observations constrain the neutron-star equation of state and provide insight into the physics of high-density matter. However, defining the tidal response in general relativity is difficult due to coordinate ambiguities and the complexity of connecting the star's response to the binary dynamics and the associated waveforms. In this paper, we show how the dynamical tidal response of a neutron star can be systematically defined within the worldline effective field theory (EFT) framework, and relate it to the gauge-invariant amplitude for gravitational-wave scattering off an isolated star. We compute this amplitude both within the EFT, using standard quantum field-theory techniques, and within stellar perturbation theory (the corresponding ultraviolet theory), solving the coupled metric and matter perturbation equations numerically in the stellar interior and matching to the analytical Mano-Suzuki-Takasugi (MST) solutions in the vacuum exterior. Matching the amplitude between the two theories fixes the dynamical tidal response. The result is consistent with known expectations, including the static limit and the behaviour near the star's resonant modes, and it recovers the imaginary part of the dominant oscillation mode induced by gravitational-wave dissipation. We conclude with a discussion of potential improvements within both the EFT and perturbation theory.

We consider a scenario for dark matter in the Universe, according to which the dark matter sector is comprised by a dark Standard Model sector which interacts only gravitationally with the ordinary Standard Model sector. This dark Standard Model sector is assumed to have the same symmetries as the ordinary Standard Model, with the couplings and the scale of the mirror Standard Model sector being different than the ordinary Standard Model sector. Specifically, the scale of the mirror Standard Model sector will be assumed to be quite higher compared to the ordinary Standard Model. Also the Yukawa couplings among the mirror Higgs and the mirror fermions are assumed to be different from those of the Standard Model and we examine the effects of the different scale and of the different Yukawas on the evolution of the Universe. As we show, a mirror world phase transition occurs at high temperatures of the baryonic Universe, which can be first order or second order, depending on the scale of the Universe and the Yukawa couplings. These are dark phase transitions which occur quite earlier than the real world Standard Model electroweak phase transition. The case of a second order phase transition is quite interesting phenomenologically, since it can potentially have a direct imprint on the spectrum of stochastic gravitational waves for frequencies probed by the future gravitational wave detectors. Also we examine whether this mirror dark matter world can form atoms and as we show in some scenario the high scale mirror dark matter can have both atomic and subatomic particle components. We also give an approximation of the total equation of state of high scale mirror DM and we discuss how high scale mirror DM can reconcile contradicting observations like the Bullet cluster and the Abell 520 cluster.

Using two distinct approaches, we derive a universal expression for the leading finite-volume effects of the smeared vector-vector spectral density (proportional to the smeared hadronic $R$-ratio) in a periodic cubic spatial volume of side length $L$. First, building on the results of previous work for finite-volume effects on Euclidean two-point functions, we show that the $L$ dependence is exponentially suppressed for a certain class of smearing kernels, and that the leading effects can be expressed universally in terms of the pion form factor. The same representation is then derived starting from the Lellouch-Lüscher-Meyer expression for the spectral decomposition of the correlator. The results may prove useful for controlling the $L \to \infty$ extrapolation of smeared spectral densities, in particular by defining a scaling regime in which the finite-volume effects are dominated by the leading terms in a large $L$ expansion and thus can be reliably estimated. To illustrate this point, we also present numerical estimates based on various kernels and models of particle interactions. Despite focusing on the vector channel, our derivation defines a general framework applicable to other cases as well.

Pseudo entropy is a complex-valued generalization of entanglement entropy defined from a reduced transition matrix. We study the pseudo entropy associated with a real-time transition matrix between an initial pure state and its unitary time evolution. For a subsystem $A$, we show that the short-time behavior of real-time pseudo entropy is governed by the correlation between the physical Hamiltonian $H$ and the modular Hamiltonian $K_A=-\log\rho_A$ of the initial reduced state, $ S_A(t,0)=S_A(0)-it \langle K_A(H-\langle H\rangle)\rangle + \mathcal{O}(t^2)$. For Hermitian dynamics, the initial imaginary response is controlled by the symmetrized covariance of $H$ and $K_A$ with an overall minus sign, while the initial real response is governed by their commutator. Thus the imaginary part of real-time pseudo entropy is not merely a branch artifact: it is a time-oriented modular response generated by the correlation between microscopic time evolution and subsystem coarse graining. We clarify the relation of this result to the known first law of pseudo entropy, derive an all-order expression in a Schmidt-diagonal model, recover thermal pseudo entropy as a special case, illustrate the covariance/commutator decomposition in a two-qubit model, and confirm the covariance response in transverse-field Ising-chain quenches, including a finite-size study of a modular susceptibility near the Ising critical region. We discuss how this amplitude-level oriented response can be related to ordinary entropy production, and also give a concrete $\mathcal{PT}$-symmetric toy-model illustration of the non-Hermitian extension.

We investigate the decoherence of a quantum spatial superposition of a static particle in Schwarzschild and Reissner-Nordström black holes. By treating the particle as a localized classical source coupled to a quantum scalar field, we reformulate the decoherence process in the Danielson-Satishchandran-Wald (DSW) gedankenexperiment through coherent state generation and derive the local expression for the decoherence functional in terms of the Wightman function. In the long-time limit, the decoherence rate is shown to be characterized by the low-frequency behavior of the Wightman function. We then employ the asymptotic matching method to calculate the analytical expressions of the Wightman functions in the Boulware, Unruh, and Hartle-Hawking vacua. We show that the decoherence behavior depends on the quantum state of the environmental field. While the Boulware vacuum gives vanishing decoherence for a static superposition, the thermal effects associated with Hawking radiation in the Unruh and Hartle-Hawking vacua can induce nonvanishing decoherence.

We investigate the quantum entanglement of Bethe states across a family of integrable spin chains, including the XXX$_{\frac{1}{2}}$ model, its higher-spin generalizations (XXX$_s$), and the non-compact $SL(2,\mathbb{R})$ chain. For on-shell eigenstates, we perform a comprehensive scan of the bipartite entanglement entropy across the entire spectrum of finite chains with periodic boundary conditions, and identify the Bethe solutions that minimize and maximize the entanglement. These extremal solutions follow systematic, spin-dependent patterns in the Bethe quantum numbers. In the XXX$_{\frac{1}{2}}$ spin chain, for the antiferromagnetic chain, the state with minimal entropy always coincides with the lowest-energy state (the ground state) within a given fixed-magnon sector. For the higher-spin XXX$_s$ model, however, the lowest-entropy state is not always identical to the ground state, and can even be the state of highest energy. By contrast, the Bethe roots that maximize entropy exhibit considerably more intricate structure. Our analysis further reveals how special Bethe root configurations, such as singular and strange solutions, affect entanglement, and it uncovers characteristic entanglement features in the non-compact $SL(2,\mathbb{R})$ chain that are absent from compact spin chains. For off-shell Bethe states, we develop an optimization algorithm that extremizes the entanglement entropy over rapidity distributions, enabling us to explore the maximum entanglement achievable by a Bethe state without imposing the Bethe ansatz equations.

We study quantum gravitational effects inside hyperbolic black holes with both outer and inner horizons by solving the Wheeler–DeWitt (WDW) equation in the minisuperspace approximation. The WDW equation contains a tachyonic region where the effective potential becomes negative. We develop a numerical method that consistently evolves the wave function across this region and obtain stable solutions throughout the entire minisuperspace. For small values of the parameter $\kappa$, which controls the strength of quantum gravitational effects, the wave packet propagates along the classical trajectory with only mild quantum spreading. As $\kappa$ increases, enhanced quantum effects lead to significant spreading of the wave packet during its propagation. Nevertheless, when the initial state is localized near the outer horizon, the wave packet becomes localized again in the vicinity of the inner horizon. We refer to this recovery of localization as a refocusing phenomenon. This result suggests that, if the geometry is classical near the outer horizon, it becomes classical again near the inner horizon. Within the minisuperspace approximation, inner-horizon formation is not obstructed by quantum gravitational effects.

We investigate the hydrodynamic properties of a strongly coupled non-Abelian plasma dual to a four-dimensional AdS black brane with a nonminimal coupling of the form $q_2 F^{(a)\alpha\beta}F^{(a)\gamma\lambda}R_{\alpha\gamma}R_{\beta\lambda}$ in the bulk action. This higher-derivative term introduces a direct interaction between the Yang-Mills field strength and the Ricci tensor, leading to corrections beyond the minimal Einstein-Yang-Mills theory. Using a perturbative expansion in the small coupling $q_2$, we construct the black brane solution up to first order and employ the fluid-gravity correspondence to compute two key transport coefficients: the DC color conductivity $\sigma$ and the shear viscosity to entropy density ratio $\eta/s$. In holography, $\eta/s$ is inversely proportional to the square of the coupling constant of the boundary theory, while $\sigma$ in Einstein-Maxwell theory satisfies a universal lower bound $\sigma \ge 1$ (in units where $\hbar=1$), saturated for uncharged black holes and characterizing a perfect quantum critical fluid. Our results reveal that the nonminimal coupling significantly alters these transport quantities. For the DC conductivity, we find $\sigma = 1 - q_2 \bigl(9\kappa Q^2/(L^2 r_h^4) + 7\kappa^2 Q^4/(4 r_h^8)\bigr)$, indicating a violation of the conductivity bound for $q_2>0$ while the bound is preserved for $q_2<0$. For the shear viscosity, we obtain $\eta/s = (1/(4\pi))\bigl(1 + q_2\, 7\kappa^2 Q^4/(2 r_h^8)\bigr)$, showing that the KSS bound is modified by a term linear in $q_2$. The sign of $q_2$ determines whether the ratio increases above or decreases below the universal value $1/(4\pi)$. These findings highlight the sensitivity of holographic transport to curvature-coupled gauge interactions and provide a controlled example of how higher-derivative corrections influence the hydrodynamic regime of strongly coupled plasmas.

We study black hole thermodynamics using a two-dimensional effective theory obtained by dimensional reduction of four-dimensional Einstein–Maxwell theory. For spherically symmetric charged black holes, the resulting dilaton gravity has a nonlinear potential that reproduces the semiclassical phase structure of four-dimensional AdS black holes, including the Hawking–Page transition and the small/large Reissner–Nordström–AdS black hole transition. This shows that the two-dimensional theory before taking the near-horizon and near-extremal limits captures non-extremal thermodynamics beyond the Jackiw–Teitelboim gravity regime. We also include electromagnetic Kaluza–Klein modes on the internal sphere and integrate them out to derive the one-loop effective dilaton gravity. At leading order in the derivative expansion, these corrections appear as constant shifts in the black hole entropy and in the effective charge parameter of the dilaton potential. Therefore, the semiclassical phase structure is not qualitatively modified within this leading local approximation.

We investigate the viability of scalar-tensor (quintessence) models of dark energy with a quartic polynomial nonminimal coupling to gravity and a linear scalar potential. The polynomial nonminimal coupling is used to ensure that the field is well stabilized in the early universe. We perform a systematic exploration of the parameter space spanned by the quadratic and quartic nonminimal couplings, as well as the slope of the potential. We confront the predictions of the model with the latest Dark Energy Spectroscopic Instrument (DESI) constraints on the dark energy equation of state and also with complementary bounds from local tests of gravity, including solar system constraints and limits on the time variation of the effective Newton's constant. We identify bands in parameter space where all these constraints are satisfied, finding such bands to be very narrow.

Assuming the gravitational field is classical and that it couples to quantum fields via the semiclassical Einstein field equations, we show that the weak-field dynamics of a massive and non-relativistic qubit can in principle be used to solve an $\mathsf{NP}$-complete problem in polynomial time. We attribute this vast computational power to the non-linear dynamics afforded by the semiclassical Einstein field equations. Consequently, the above two assumptions entail a violation of the Physical Extended Church–Turing Thesis, which we regard as evidence for the quantization of gravity.

Motivated by the recent interest in multipoint Padé approximants in the physics community, we discuss Chebyshev rational functions and show how they give rise to multipoint Padé approximants in exactly the same way that Chebyshev polynomials produce Padé approximants. We present recurrence relations for Chebyshev rational functions, as well as the underlying continued fraction of Thiele type (also known as $R_{II}$ type). Finally, we provide numerical evidence illustrating the effects of noise on this interpolation scheme and show that a phenomenon similar to that recently observed by Costin, Dunne, and Meynig for Padé approximants also occurs in the multipoint setting.

Quantum Chromodynamics (QCD) provides a remarkable realization of how quantum effects reshape the symmetries of a classical field theory. The axial anomaly links chirality to gauge-field topology and underlies the resolution of the $U(1)_A$ problem, while the trace anomaly generates the intrinsic QCD scale through dimensional transmutation and accounts for most of the mass of hadrons and hence visible matter. Together, these quantum effects reveal the central role of gluonic dynamics and vacuum structure in strong-interaction physics. In this review, we discuss the theoretical foundations and physical consequences of anomalous symmetry breaking in QCD. We examine anomalous Ward identities, the topological structure of gauge fields, instantons, topological susceptibility, and the realization of chiral and scale symmetries in the QCD vacuum. We review their role in the generation of hadron masses, the $\eta'$ mass, and the resolution of the $U(1)_A$ problem, and discuss their manifestations in polarized deep inelastic scattering, nucleon spin structure, and modern studies of hadron structure. Particular emphasis is placed on recent developments connecting vacuum topology, the flavor-singlet axial charge, topological screening, and the proton spin problem. Our aim is to provide a unified perspective on how quantum anomalies connect vacuum structure, hadron properties, and partonic observables, bridging nonperturbative dynamics and perturbative QCD.

We study holographic entanglement entropy in Coulomb-branch solutions describing spherical shells of D$p$-branes. The corresponding throat geometries contain a flat-space bubble in the infrared region, providing a concrete top-down framework for exploring holographic entanglement of flat space. We find that the flat-space region is associated with a reduction of entanglement and of the effective infrared degrees of freedom in the dual boundary state relative to the standard vacuum. We also examine internal RT surfaces and holographic complexity, and show that they exhibit similar qualitative behavior. Finally, we comment on the broader implications of our results for flat space holography.

Building on two key ingredients, namely the well established gauge-theoretic formulation of gravity and the observation that the tangent space of a curved manifold need not have the same dimension as the manifold, we discuss how all known fundamental interactions can be accommodated within a single unified framework. The unification is realised by enlarging the tangent group of the four-dimensional spacetime manifold to $SO(2,16)$, a choice that simultaneously encompasses both the gauge group underlying the gravitational sector and the $SO(10)$ Grand Unified Theory for the internal interactions. The gravitational theories entering this construction are Conformal Gravity and Fuzzy (Noncommutative) Gravity, each formulated in gauge-theoretic terms.

Stabilizer Rényi entropy has emerged as a probe of nonstabilizerness in quantum many-body systems, but its scaling structure beyond critical points remains poorly understood compared with entanglement entropy. Recent field-theory approaches indicate that stabilizer entropy contains universal critical data and boundary-sensitive terms, raising the question of how these structures extend into massive and crossover regimes. We address this problem for a broad class of finite-range spin chains at Rényi index one-half. We derive exact finite-size formulas for both full periodic chains and finite intervals of the infinite chain, making the universal crossover from critical to noncritical behavior analytically accessible. In periodic geometry, the entropy obeys a volume law away from criticality and exhibits a universal finite-size crossover controlled by the competition between system size and correlation length. We also show that the large-scale SRE density develops a cusp across the field-tuned critical line, while the XX endpoint is governed by a distinct scaling regime associated with the saturation point. In the subsystem geometry, the interval entropy separates bulk critical behavior from boundary contributions generated by the way the finite region cuts the infinite chain. The crossover from critical to massive behavior is then encoded in boundary constants and universal functions controlled by the correlation length. Through exact stabilizer-entropy correspondences, the scaling theory extends to internal XY reductions, Finite-range spin chains, and Cluster–Ising representatives. Our results provide an exact lattice benchmark for the emerging QFT description of stabilizer entropy beyond isolated conformal points.

We study the renormalization-group flow of higher-dimensional fermionic interactions $(\psi^\dagger \psi)^{2n}$ in the presence of a Fermi surface. We show that the growth of the BCS four-fermion coupling induces a drag mechanism whereby higher-order fermionic couplings are driven to strong coupling in the infrared. We derive the corresponding beta functions and show that the drag effect applies generically to the whole tower of fermionic operators. Remarkably, although all couplings are driven toward the same strong-coupling scale, the renormalization-group flow preserves a hierarchy in which higher-dimensional operators remain parametrically suppressed relative to the BCS interaction. We then investigate this mechanism in a $2+1$-dimensional non-Fermi liquid coupled to a critical boson. While higher-order fermionic interactions are similarly enhanced along the flow, we show that they do not destabilize the IR stable non-Fermi-liquid fixed point, present for sufficiently large $N$. We briefly discuss possible implications for multicomponent superconductors and other strongly correlated metallic systems.

We investigate a representative set of static solitonic solutions of the Einstein-Proca theory in the Newtonian regime, where the field frequency approaches the particle mass, $\omega \to \mu$, and compare them with the corresponding solutions of the spin-1 Schrödinger-Poisson system, which provides the effective description in this limit. While this correspondence is relatively straightforward in the Einstein-Klein-Gordon case, the vector nature of the Proca field, combined with the enhanced $U(3)$ symmetry of the nonrelativistic spin-1 regime, gives rise to several nontrivial features that require careful analysis. We establish a mapping between the two descriptions by identifying $\ell=0$ electric Proca stars with radially polarized (hedgehog) configurations and $\ell=1$ electric Proca stars with linearly polarized configurations. We further clarify some aspects of the ground state and resolve several apparent discrepancies between relativistic and Newtonian solutions, particularly concerning their morphology and stability properties. An important conclusion of this work is that the nonrelativistic regime supports a richer spectrum of stable equilibrium configurations than the relativistic theory, including stable excited states.

We study the thermal transition between the bounce and the sphaleron in quantum mechanics with a metastable vacuum from the viewpoint of Borel resurgence. For two models representing a second-order and a first-order transition, we compute the perturbative expansion of the thermal free energy to high orders and extract the leading Borel singularity data $(A,b,S)$ as functions of temperature. The Borel singularity location $A$ reproduces the on-shell action of the dominant saddle on both sides of the transition, joining smoothly in the second-order case and developing a kink in the first-order case. The characteristic exponent $b$ jumps between $0$ and $1/2$ across the transition, counting the zero modes of the corresponding saddle. The Stokes constant $S$ matches the one-loop determinant around the saddle. The perturbative expansion around the false vacuum thus determines the transition temperature, the order of the transition, and the decay rate including the one-loop prefactor without relying on semiclassical inputs.