Papers

We show how the synergy of scaling and non-overlapping global symmetries can lead to Renormalisation Group Invariants (RGIs) among the parameters of potentials with multiple scalars. The instrumental role of scale-invariant field directions in the identification and construction of RGIs for bilinear field operators to all loops is demonstrated. We present a few illustrative examples to showcase our constructive spurion-field approach, which is applied to simple non-supersymmetric models as well as to scenarios reported recently in the literature that include the two-Higgs doublet model. The problematic issues of RGIs to address the gauge-hierarchy problem beyond supersymmetry are discussed.

[Abridged] In slow roll inflation, the power spectrum (PS) of primary gravitational waves (PGWs) generated from the quantum vacuum rises as $k^2$ over wave numbers $k$ which never leave the Hubble radius. In fact, over such small scales, the PS exhibits a similar behavior at any time after inflation. In a recent work, we had argued that the PS of PGWs has to be regularized to truncate the unphysical quadratic rise at large wave numbers. Assuming instantaneous transitions from inflation to the epochs of radiation and matter domination, we had shown that the regularized PS oscillates with a constant amplitude about a vanishing mean over small scales during these epochs. We had also smoothed the transition (actually, the `effective potential' governing the equation of motion of GWs) from inflation to radiation domination using a linear function and evaluated the regularized PS of PGWs post inflation. In such a case, we had shown that, over small scales, while the regularized PS continues to oscillate about zero, its amplitude decreases as $k^{-1}$. In this work, using the Born approximation, we examine the behavior of the regularized PS of PGWs over small scales when they are evolved through smoother and smoother transitions from inflation to the epochs of radiation and matter domination. We illustrate that, at small scales or high frequencies, the suppression in the regularized PS of PGWs occurs more and more sharply as the transition is smoothed further and further. With the help of examples, we also show that, in the case of transitions described by infinitely differentiable `effective potentials', the regularized PS of PGWs exhibits an exponential suppression on small scales. We argue that the observation of the exponential drop in the PS of PGWs can help us determine the energy scale and the time of the end of inflation. We clarify related issues and discuss the wider implications.

In this thesis we analyze the quantum vacuum properties of non-abelian gauge theories. We calculate the energy of the quantum vacuum by non-perturbative methods using Monte Carlo simulations, focusing on the contribution of boundary effects to the Casimir energy. In particular, we analyze the dependence of the vacuum energy on the types of boundary conditions. The main goal is to clarify the behaviour of this energy for large separation L between the boundaries of the domain where the fields are confined. Usually this Casimir energy decreases polynomially with L for massless theories and exponentially for massive theories. Since gauge theories interpolate between these two regimes, being massless in the ultraviolet regime and massive in the infrared regime, one expects a very special change of behaviour from the perturbative to the non-perturbative approaches. In pure gauge theories there is evidence of the existence of glueball states in the low energy spectrum with a non-vanishing mass, the second goal will be testing if the mass of the lightest glueball is responsible for the exponential decay of the Casimir energy of gauge theories.

Integrable field theories exhibit infinitely many symmetries which underlie their solvability, but the structure of these symmetries can become obscured after performing an integrable deformation such as $\TT$ or an auxiliary field deformation. In this paper, we present a systematic organizing principle for understanding deformed charges and their Yangian structure in a broad class of integrable sigma models and their auxiliary field deformations. We generalize the recursive procedure of Brezin, Itzykson, Zinn-Justin, and Zuber (BIZZ) for generating non-local charges, and give sufficient conditions under which the resulting charges obey a Yangian algebra. We apply these results to many examples of integrable sigma models and their auxiliary field deformations, finding a Yangian algebra and Maillet bracket structure in all cases. This offers a unified explanation for the persistence of Hamiltonian integrability and Yangian symmetry across a wide landscape of deformed sigma models.

We reassess the consistency conditions for a hypothetical population of primordial, electrically charged compact objects, here called astrons. This paper formulates astrons not as a completed model, but as a set of quantitative consistency tests for a primordial large-charge compact-object scenario. The fiducial phenomenological parameters, \(M_A\sim10^{12}M_\odot\), \(Q_A\sim4\times10^{32}\,\mathrm{C}\), and megaparsec-scale separations, are treated as a benchmark to be tested rather than as an established outcome of the model. We show explicitly that ordinary accretion-driven charge separation produces charges only of order \(10^{11}\)–\(10^{14}\,\mathrm C\) for this mass, leaving an 18–21 order-of-magnitude gap relative to the fiducial branch. Thus the large-charge branch, if it exists, must arise from a primordial charge-concentration mechanism not supplied by the minimal capture model. Likewise, the failure of linear Debye–Hückel screening in the enormous electrostatic potential of an astron does not demonstrate charge survival; it identifies a nonlinear neutralization and kinetic-transport problem. Finally, a cosmologically relevant abundance of \(10^{12}M_\odot\) compact objects requires mean separations of several megaparsecs and must satisfy discreteness, Poisson-power, clustering, and dynamical constraints. The homogeneous Coulomb interaction energy scales as \(a^{-4}\), so it cannot by itself act as a late-time cosmological constant. \begin{refone}Moreover, the Lorentz force acts directly only on charged astrons, not on the no-net-charge population of galaxies, photons and neutral dark matter. Any viable cosmological implementation must therefore derive a metric-level or domain-averaged acceleration shared by the neutral cosmic flow, rather than merely a pairwise repulsion among charged sources.

We show that the emergence of time evolution in an otherwise timeless nonrelativistic closed quantum system – viewed as a poor man's model of generally covariant quantum theory – can be understood from the perspective of the path integral representation. As often happens in the functional integral approach, this viewpoint offers a more intuitive account of features that become cumbersome in the operator/Hilbert-space formulation. We show how Schrödinger evolution emerges once a clock degree of freedom is identified and placed in a suitable semiclassical `good-clock state'. Our analysis has a consequence that extends to path integral formulations of generally covariant systems with action $S$ (including gravity). In such theories certain transition amplitudes take the form $\exp(iS/\hbar)+\exp(-iS/\hbar)$ rather than the expected `forward propagating' $\exp(iS/\hbar)$. This feature, known as the cosine problem, appears in concrete regularizations of the path integral, for example in the spin foam representation defining the physical inner product between spin network states in loop quantum gravity. Both formally and in explicit regularizations, this apparent difficulty has led some authors to seek modifications of the basic amplitudes to eliminate backward propagation. Our model shows that the cosine problem is instead a natural consequence of time-reversal invariance of the fundamental dynamics together with the time-neutral boundary states commonly used in transition amplitudes. When a suitable clock system is identified and placed in a semiclassical `good-clock state', it introduces a time arrow selecting the `forward propagating' $\exp(iS/\hbar)$, without modifying the fundamental dynamics. The analysis clarifies how time emerges under suitable conditions and emphasizes that, in the canonical formulation, quantum gravity is fundamentally timeless.

We identify a superspace mechanism behind equivariant localization in supergravity. We show that closed superforms generate, on supersymmetric backgrounds, equivariantly closed polyforms. After presenting the general mechanism, we construct such polyforms for vector and linear multiplets, and for chiral and BF action principles, in off-shell $4d$ $\mathcal{N}=2$ conformal supergravity, reproducing and extending recent results. Our construction provides a geometric first step toward equivariant localization of BPS observables in supergravity, including higher-derivative theories, and holography.

Monte Carlo event generators are central to high-energy physics analysis. However, workflows based on handwritten scripts can be difficult to reuse, modify, and reproduce when multiple Monte Carlo models, tune variations, run variations, and output formats are involved. We present MAGE-HEP, short for Monte Carlo Analysis and Graphical Environment for High-Energy Physics, a Graphical User Interface (GUI) driven workflow environment for reproducible Monte Carlo-based analyses in high-energy physics. MAGE-HEP organizes analysis workflows through a project-study-run hierarchy. The project stores the workspace, the study stores the reusable analysis context, and each run represents a controlled execution of that context. The MAGE-HEP Node API provides the analysis-building layer for defining generator configurations, observables, selections, output rules, and generated C++/ROOT analysis code. A study context can be inspected, reused, or exported as a .mcx context bundle, while the project state can be exported as a portable .mgp bundle. The current beta implementation validates the core idea using a PYTHIA8 and ROOT workflow. It includes background execution, manifest-based run tracking, live ROOT inspection, and particle-table summaries for supported output layouts. This paper describes the architecture, workflow, and current beta implementation of MAGE-HEP.

This work presents a new class of exact analytic rotating black hole solutions within five-dimensional generalized Proca theories. Through a Kerr-Schild ansatz where the Proca field is set along a null geodesic congruence, the non-linear field equations reduce to a consistent set of three master equations. This geometric configuration ensures that the vector field remains light-like on-shell, effectively restricting the theory's functional couplings to discrete constants and allowing for a fully analytic treatment. The resulting solutions, incorporating a cosmological constant and two independent angular momenta, exhibit primary hair given by an arbitrary function of the non-Killing angular coordinate. We identify several solution branches defined by specific algebraic relations between the Proca coupling constants, providing a significant generalization of the Myers-Perry family. Notably, the metric retains a Kerr-Schild form identical to the Myers-Perry representation, with an additional contribution constructed from the tensor product of the Proca one-form with itself.

Kerr quasinormal modes near algebraically special frequencies exhibit anomalous behavior, including apparent bifurcation, disappearance, and a nonsmooth connection to the Schwarzschild limit, which has remained puzzling for decades. Tracking poles and zeros of Green-function building blocks across different Riemann sheets, we show that the bifurcation is due to an avoided crossing accompanied by resonant excitation, while the disappearance is due to pole skipping caused by cancellation of a quasinormal-mode pole by a Matsubara-mode zero. This resolves the physical origin of these long-standing anomalies.

A Lagrange multiplier field restricts the quantum corrections to the Einstein-Hilbert action at one-loop order, yielding a model that is renormalizable and unitary while reproducing the Einstein field equations in the classical limit.

In this work we address the possibility of having a positive running of the spectral index in inflationary theories. The recent ACT data indicate mildly that the running of the spectral index might be positive, and several other physical indications point out this possibility. If the running of the spectral index is confirmed to be positive by future cosmic microwave background experiments, this can rule out quite popular inflationary scenarios. We investigate how it is possible to obtain a positive running of the spectral index in the context of minimally coupled scalar field gravity and modified gravity. For the modified gravity we choose two mainstream and of string origin candidate theories, $F(R)$ gravity and Einstein-Gauss-Bonnet gravity. In the case of scalar field inflation and $F(R)$ gravity inflation, we demonstrate the difficulties for obtaining a positive running of the spectral index for a viable inflationary regime, so scalar theories and $F(R)$ gravity are mostly compatible with the Planck data. But nuanced scalar field scenarios can be compatible with the ACT data and produce a positive running of the spectral index. In the context of Einstein-Gauss-Bonnet theories which are compatible with the GW170817 event, the running of the spectral index can easily be positive while in parallel having a viable inflationary era.

The differential equations satisfied by the wavefunction coefficients of conformally coupled scalars in a power-law cosmology can be recast as an iterative differential system of basis functions. These functions can be encoded within graph tubings and are governed by a set of rules describing how they flow in kinematic space. In this paper, we formulate a set of splitting rules equivalent to the kinematic flow at tree level by reversing the flow direction of graph tubings. Specifically, for any basis function, these rules identify all other basis functions whose total differentials contain it. From the splitting perspective, we uncover deeper physical information captured by graph tubings, such as the formation of singularity structures and the realization of local evolution. In an alternative basis based on time ordering, the splitting processes correspond to the emergence of time integrals. These rules can also be generalized naturally to the $\mathrm{tr}\,\phi^3$ theory beyond individual graphs, providing a physical interpretation of the structure of the associahedron. This suggests that graph tubings and the kinematic flow may be more fundamental objects than the differential equations, and may have a life of their own.

We study the classification problem for anomaly-free 6D $\mathcal N=(1,0)$ supergravities with a gauged abelian R-symmetry and one tensor multiplet. We present eleven new models with gauge group $G_{\mathrm{non-Abelian}}\times U(1)_R$ that satisfy the local Green–Schwarz factorization condition, together with several recently proposed global consistency conditions. In particular, the low-rank models we found are precisely where some of the recent enumeration literature is least directly applicable. These examples suggest that the landscape of anomaly-free gauged $U(1)_R$ supergravities may be richer than previously recognized while still remaining highly constrained. We analyze the arithmetic structure of the anomaly coefficients, including their integral pairings, embeddability into rank-two unimodular charge lattices, the characteristic-vector condition and ghost-free gauge-field conditions. We show that $n_V \equiv 8 \pmod{12}$ is necessary and sufficient for the unimodular embeddability in the rank-two case, when the gauge group does not contain $SU(2)$, $SU(3)$ and $G_2$. For the characteristic-vector condition we verify sufficiency for the branches realized by our examples and identify a remaining branch requiring additional exclusion. We also present a detailed discussion of the contribution to the anomaly polynomial when the $D_4$ Lie algebra is present. These results sharpen the boundary between anomaly-free 6D spectra, global-consistency constraints, and possible UV realization in string theory or F-theory.

We consider an inverted harmonic oscillator in the space $L^{2} (\mathbb{S})$ of square-integrable functions on the circle $\mathbb{S}$ and compute its density of states employing the stationary phase approximation. Our computation is based on an oscillatory integral representation of the Schwartz kernel of the time-evolution operator. This demonstrates thermalisation as a semi-classical manifestation of the classical Lyapunov instability – reported earlier in [Phys. Rev. D 102, 044006; Phys. Rev. D 102, 124047] using heuristic analytic continuation. Our spectral analysis of the Hamiltonian points out and closes the conceptual and mathematical gaps in the preceding literature.

The theory of thermal fluctuations in crystalline membranes is put under scrutiny. In particular, the two critical regimes of the renormalisation group diagram, which are often left out of the discussion because of their instability in one direction, are examined in details. After studying the proper Goldstone mode counting around each of them, the properties of the fluctuations dominating the large scale spectrum are analysed. This shows that the fixed point P2 is a good candidate to describe the melting of a crystalline membrane. The properties of the melted membrane are then compared to the known properties of fluid membranes. As a byproduct of this analysis, we show that the generation of a fluid membrane by melting a bidimensional crystal allows to formulate its correlation functions without being plagued by the ghosts that inevitably show up in the usual Canham-Helfrich action relying on the Monge parametrisation.

In holography, the complexity–momentum correspondence relates the increasing momentum of a point particle falling into an eternal black hole to the rate of growth of the Krylov complexity of the dual boundary state, a conjecture established exactly for the BTZ black hole in AdS$_{3}$ at the semiclassical level. We examine possible extensions of the correspondence by considering boundary higher Krylov complexities and Krylov correlators encoding fluctuations and temporal correlations of the spreading quantum state. To this end, we derive exact results for Krylov correlators in quantum systems with $\mathfrak{sl}(2,\mathbb{R})$ or Heisenberg-Weyl symmetry and apply them to the complexity–momentum correspondence. We show that certain out-of-time-ordered correlators of two or more Krylov speed operators at different times are proportional to combinations of the proper radial momenta of a particle falling into the BTZ black hole in AdS$_{3}$, evaluated at those times. This represents a first step in the generalization of the original complexity–momentum relation.

This Letter shows that a supersymmetric structure is inherent to the time space inverted (TSI) quantum mechanics (QM) framework, where the spatial evolution of states is generated by the operator $\hat{\mathcal{P}}^{\pm}(\hat{\mathcal{H}},\hat t;q)=\pm\sqrt{2m[\hat{\mathcal{H}}-\mathcal{\hat V}(q)]}$ [\href{https://doi.org/10.1103/PhysRevA.95.032133}{Phys. Rev. A. 95, 032133 (2017)}], named here Momentunian, whose square-root structure that can be factorized. Such factorization leads directly to a supersymmetric algebra with supercharges and partner Hamiltonians. For the relativistic Momentunian the zero mode states are shown to be evanescent states, independent of the physical potential. Furthermore, the existence of non-relativistic and relativistic Momentunian partners is demonstrated, whose zero-mode states are no longer necessarily zero energies, but vanishing momenta states. The natural emergence of the $1/2$-fractional time derivatives in the TSI QM, leads to supercharges which incorporate memory effects into the supersymmetric wave functions. Results indicate that supersymmetry emerges as a structural property of the TSI QM rather than being imposed phenomenologically.

We study the Joule-Thomson expansion and extended thermodynamics of a modified black hole characterised by the parameters $\alpha$, $\beta$, and $\sigma$. Analysis of the Hawking temperature, Joule-Thomson coefficient, inversion curves, and isenthalpic trajectories shows that these parameters significantly modify the heating-cooling behaviour and thermal stability of the system. The deformation parameter $\alpha$ and control parameter $\beta$ shift the temperature minimum, enlarge the cooling region, and raise the inversion temperature, while $\sigma$ produces a weaker but consistent influence. The heat-engine analysis reveals that $\alpha$ enhances efficiency, whereas higher $\beta$ and $\sigma$ reduce it. Overall, the results demonstrate that geometric deformation and quintessence jointly govern the unified thermodynamic structure of the black hole.

In this work, we explore holographic entanglement entropy in the QCD phase diagram under an external magnetic field using an Einstein-Maxwell-dilaton model. We consider both the specious-confinement and deconfined phases. In the perpendicular magnetic field orientation, the strip length shows three distinct branches, and the entanglement entropy develops a swallow-tail structure, indicating a transition between connected and disconnected entanglement surfaces. For the parallel orientation, the behavior is monotonic and no transition occurs. In addition, the difference in entanglement entropy changes smoothly with temperature at small chemical potential, but becomes multivalued at large chemical potential. Increasing the magnetic field restores single-valued behavior. These results are consistent with the black hole thermodynamics and the QCD phase diagram. Our findings show that entanglement entropy can serve as an effective probe of the QCD phase transition.

We prove a threshold-sharp stability theory for the conformal scalar-curvature sector on zero-curvature Carter backgrounds. The main result is a fully closed bounded-slab theorem: the reflecting evolution is constructed, the conserved energy is proved positive, the complete affine threshold obstruction is identified, and all remaining finite-energy dynamics are shown to be uniformly stable with no unstable modes. This is the sharp statement for compact reflecting slabs, where genuine time decay is false in general. We then extend the same threshold philosophy to black-hole exteriors, separating the intrinsic conformal mechanism from the exterior scalar-wave inputs needed for red-shift, local energy, limiting absorption, and zero-frequency control. The framework gives main applications to Kerr, Reissner-Nordström, slowly rotating weakly charged Kerr-Newman wall exteriors, and extremal horizon-charge obstructions. Our precise result is that it proves stability only for the conformal scalar-curvature sector, not tensorial or nonlinear gravitational stability, and it distinguishes boundedness, qualitative local decay, polynomial decay, and extremal Aretakis-type obstruction without conflating them.

We establish a geometric correspondence between the Functional Renormalization Group (FRG) and a Ricci flow modified by a potential-driven diffeomorphism. By rewriting the Polchinski exact RG equation as an infinite-dimensional Fokker–Planck equation for field-distribution functionals, we show how a probability flow driven by a “thermodynamic” free-energy functional induces the evolution of the Fisher information metric on the coupling-constant manifold. Using the continuous scale-dissipation rate of this free-energy functional, we construct an RG-flow entropy functional that provides an infinite-dimensional counterpart of Perelman's \(\mathcal{F}\)-entropy. The parametric Hessian of this RG-flow entropy then encodes the scale deformation of the Fisher information metric, thereby linking the JKO–Wasserstein flow in field-configuration space to the geometry of the coupling-constant manifold. An emergent scalar information potential \(\Phi\) encodes the potential-driven diffeomorphism component, restoring the tensorial form of the flow under reparametrizations of the coupling coordinates. In this representation, the successive integration of high-energy degrees of freedom effectively smooths out the curvature of the information manifold, so that RG fixed points are realized as steady Ricci soliton equilibria. These results connect quantum field theory, optimal transport, and Perelman's theory of geometric evolution, providing a geometric framework for characterizing the stability, universality, and topological structure of quantum field theories.

We present a holographic dual description for the O(N) vector model in $d$-dimensional Euclidean space within the functional renormalization group (FRG) framework. By iterating Wilsonian renormalization group transformations, the extra-dimensional scale coordinate is identified as the radial direction of an emergent $(d+1)$-dimensional bulk spacetime. We construct a bidirectional holographic dictionary in which the emergent bulk metric is determined by the spectrum of the non-perturbative $GG$ polarization function. Using this dictionary we show that as the mass gap decreases, the emergent geometry evolves from a Ricci flat to an Anti-de Sitter $(AdS_{d+1})$ geometry.

We study cold dense single-flavor $\mathrm{SU}(2)$ gauge theory in $(1+1)$ dimensions in the thermodynamic limit using a gauge-invariant variational uniform matrix product state ansatz. This formulation provides a sign-problem-free, first-principles approach to dense QCD. We show that, at finite baryon density, the infrared behavior is consistent with a Tomonaga–Luttinger liquid: the central charge is determined to be $c=1$, and the two-point function of the baryon-number density exhibits spatial modulation with the wavenumber predicted by Tomonaga–Luttinger liquid theory. The Luttinger parameter varies smoothly from $K\simeq 1$ in the dilute-baryon regime to $K\simeq 1/2$ at higher densities, suggesting a quarkyonic crossover. Furthermore, the quark distribution reveals the coexistence of a quark Fermi sea with a baryonic infrared description, thereby realizing the quarkyonic picture from first principles.

We study the nonlocal effective action of a massless scalar field defined on a flat manifold with a curved boundary. Using a heat-kernel approach, we derive a covariant expansion of the nonlocal contribution to quadratic order in the extrinsic curvature tensor. Our construction provides a geometric framework that both reproduces earlier results obtained for Monge-patch embeddings and extends them to more general surfaces that need not admit a global Monge-patch description. The expansion is valid in the regime where gradients of the extrinsic curvature dominate over nonlinear curvature effects. As an application, we compute the particle-creation rate for an oscillating deformed ring in $2+1$ dimensions and an oscillating deformed sphere in $3+1$ dimensions.

We calculate the three-loop master integrals contributing to the three-loop five-point amplitude on the special Coulomb branch of $\mathcal{N}=4$ SYM theory. For the genuine pentagon integrals, we follow the approach of Ref. [JHEP 12 (2025) 107], which includes a regularization preserving dual conformal invariance (DCI). As a new ingredient, we introduce a simple method, allowing to factor out the dependence on the DCI cross ratios from the contribution of each region. The remaining integrals are then essentially simplified by taking successive limits of vanishing external invariants. For 3 out of 82 regions contributing to the most complicated integral $\mathcal{I}_5^{(3)}$ we were not able to perform the integration even after these simplifications. For these three regions, we perform the integration-by-parts (IBP) reduction in parametric representation and evaluate the resulting locally finite integrals using HyperInt.

We present a three-loop analysis of the scattering amplitude of five nearly massless W-bosons in planar maximally supersymmetric Yang-Mills theory. The basis of the master integrals is established, making use of the unitarity-cut sewing technique in six-dimensional N=(1,1) super-Yang-Mills theory. Its dimensional reduction down to four allows us to generate masses for internal and external states. We descend on the special Coulomb branch of maximally supersymmetric Yang-Mills theory by setting all propagator masses to zero. Employing explicit expressions for all integrals that we calculated in a companion paper, we find a concise representation for this infrared-sensitive observable. We confirm its exponentiation, both for infrared and finite terms. The infrared double logarithm manifests the anticipated universality through the octagon anomalous dimension as its governing coefficient. Unlike our previous two-loop result, this consideration reveals that each of the three independent kinematic structures furnishing the amplitude possesses its own function of 't Hooft coupling.

We study the gauging of invertible symmetries, particularly in 3 dimensions, using equivariantisation, $G$-crossed braided zesting, and the generalised orbifold construction. We discuss how these methods are related and illustrate them in various examples. We cover all $\mathbb{Z}_2$-symmetries in Dijkgraaf–Witten $\mathbb{Z}_2$-gauge theory $\mathcal{D}(\mathbb{Z}_2)$, the $\mathbb{Z}_2$-symmetries described by Tambara–Yamagami categories, and obstructions to gauging the central symmetry in Chern–Simons $\mathrm{SU}(2)_k$-gauge theory. We introduce zested orbifold data for symmetries related by zesting and show that the two associated orbifold data are Morita-equivalent, i.e.\ they have the same underlying surface defect.

We investigate the nonlinear response of the chiral magnetic current to an external magnetic field in a holographic setup. Using the D3/D7 brane system, where the chiral magnetic effect (CME) can be realized by considering rotating probe D7-branes, corresponding to introducing an axial chemical potential, we analyze the current-magnetic field relation beyond the linear regime. Focusing on the vicinity of the phase boundary between the insulating phase and the CME phase, we find that the chiral magnetic current exhibits a multi-valued dependence on the magnetic field, indicating a highly nonlinear response characteristic of this model. We further study the dynamical stability of the insulating phase near the transition point, and show that the presence of both an axial chemical potential and an external magnetic field cooperatively stabilize the system. Our results clarify the interplay between the axial chemical potential and the magnetic field in determining the phase structure and stability of the system, and reveal new nonlinear aspects of chiral transport in holographic gauge theories.

We investigate the warm inflationary scenario in the Weyl geometric gravity theory, in which the action is constructed by adding matter to the simplest conformally invariant gravitational action in Weyl geometry. The $\tilde{R}^2$ theory can be formulated equivalently as a linear theory supplemented by an additional scalar degree of freedom originating from higher-order curvature terms, with the equations of motion obtained via variational methods. We investigate the cosmological implications of the theory by considering the warm inflationary scenario of the early evolution of the Universe, in which radiation, the inflaton field, and the Weyl vector coexist. We consider the widely studied linear dissipation coefficient model along with a quartic potential, and investigate the influence of the Weyl vector term on the dynamics. We have performed numerical computations for different coupling models, and we have successfully developed a warm inflationary model in which the Universe transitions naturally from an inflationary epoch to a radiation-dominated era. The relevant cosmological observables have been calculated and compared with the latest observational constraints from the ACT data.