Papers

Effective field theories for cosmology offer a powerful framework to investigate the dynamics of space–time and address longstanding open puzzles. In this work, we initiate a programme to analyse the ultraviolet completion of vector–tensor quantum field theories within the asymptotic safety paradigm, focusing on generalised Proca theories with a vector condensate. This enables us to assess whether a consistent fundamental UV completion exists and to constrain the set of viable infrared scenarios. Using the non–perturbative functional renormalisation group, we identify several fixed points, including Proca–type candidates, and, among them, a particularly remarkable one with four relevant directions: two associated with gravity and two induced by matter. This provides evidence for the non–perturbative renormalisability of vector–tensor theories. We further outline how the resulting UV critical surface constrains late–time cosmology.

This overview of the study arXiv:2407.18845, regarding the possibility of generating gravitational waves from a curvature-induced phase transition of a non-minimally coupled scalar dark matter field with a Higgs-portal, was showcased at the "Workshop on Standard Model and Beyond 2025" of the Corfu Summer Institute 2025. The phase transition dynamics during the transition from inflation to kination were calculated for various inflationary scales, considering both positive and negative values of the non-minimal coupling, while also examining the potential for triggering electroweak symmetry breaking. Notably, kination enhances the GW amplitudes, significantly restricting the viable parameter space. While the GW spectra follow the usual rule for high-frequencies from high inflationary scales, certain regions of the parameter space allow for a potential detection with future experiments.

We explore the Mellin space representation for the collinear limit of $N$-point energy correlators in ${\cal N}=4$ super-Yang-Mills theory. We show that these correlators can be written as integro-differential operators acting on star integrals: one-loop $n$-gons in $n$ dimensions. For the three-point energy correlator, we obtain the Mellin representation, use it to relate the correlator to the massive box integral, and show how to solve this relation to match with the expected result. For the four-point energy correlator, we obtain the Mellin representation and use it to write the correlator to a sum of various box and hexagon integrals in special kinematics. Our results provide a systematic method to relate higher-point energy correlators in the collinear limit to star integrals, which are known exactly.

We investigate the thermodynamics, photon sphere, and dynamical stability of an AdS Ayón–Beato–García (ABG) massive black hole with graviton mass and magnetic charge. The Gibbs free energy exhibits distinct limiting behaviors: it reduces to that of an AdS massive black hole when magnetic charge vanishes, to that of an AdS ABG black hole when graviton mass is zero, and smoothly interpolates to the AdS massive Reissner-Nordström case in the asymptotic regime. Furthermore, the photon sphere and shadow analysis indicate that increasing the graviton mass expands their radii, while increasing the magnetic charge causes contraction, in agreement with earlier studies of black hole spacetimes. Quasinormal mode (QNM) calculations further confirm dynamical stability, as the imaginary part remains negative, ensuring decay of perturbations. Additionally, the real part of the frequency decreases with graviton mass, while the imaginary part initially grows before saturating at higher values. Together, these results provide meaningful insights into the interplay between graviton mass, magnetic charge, and stability, thereby enriching the understanding of black holes in modified gravity theories.

Universal $T$-matrices, or Hopf algebra dual forms, for quantum groups are revisited, and their contraction theory is developed. As a first illustrative example, the (1+1) timelike $\kappa$-Poincaré $T$-matrix is explicitly worked out. Afterwards, motivated by recent results on the role of the Hopf algebra dual form of a quantum (1+1) centrally extended Galilei group as the algebraic object underlying non-relativistic quantum reference frame transformations, a new quantum deformation of the (1+1) centrally extended Poincaré Lie algebra is obtained, and its universal $T$-matrix is presented. Finally, the Hopf algebra dual form contraction is applied to this Poincaré $T$-matrix, showing that its corresponding non-relativistic counterpart is precisely the Galilei $T$-matrix associated with quantum reference frames. In this way, the Poincaré Hopf algebra dual form introduced here stands as a natural candidate for describing the symmetry structure of relativistic quantum reference frame transformations. In the appropriate basis, the associated quantum Poincaré group is recognized, remarkably, as a non-trivial central extension of the (1+1) spacelike $\kappa$-Poincaré dual Hopf algebra.

Abelian flavor charges on right-handed fermions produce left-handed anarchy: we prove that all abelian discrete Froggatt-Nielsen models with uncharged left-handed doublets yield Haar-random PMNS and CKM matrices, regardless of $\mathbb{Z}_N$ group order, charge assignment, or Majorana mass structure. Scanning $\mathbb{Z}_3$ through $\mathbb{Z}_7$ with 12 charge assignments and $10^5$ Monte Carlo samples each, we demonstrate that the mass spectrum failure previously identified for $\mathbb{Z}_3$ – the seesaw over-suppression mechanism that pushes $\Delta m^2_{21}/\Delta m^2_{31}$ to $\sim 10^{-11}$ – is specific to $\mathbb{Z}_3$ and avoidable for $N \geq 4$. The mixing angle failure, however, is universal and irreducible. The PMNS angles from every abelian model are statistically consistent with Haar-random unitary matrices, with median $\sin^2\theta_{12} \approx \sin^2\theta_{23} \approx 0.50$ and $\sin^2\theta_{13} \approx 0.31$ across all models tested. The same applies to the CKM: the joint probability of achieving CKM-like mixing from generic $O(1)$ coefficients is $< 2 \times 10^{-6}$. We identify the algebraic origin of this obstruction: abelian groups have only one-dimensional representations, so each generation transforms as an independent singlet with 18 free parameters for three Dirac mass matrices – far exceeding the 10 physical observables. The transition to non-abelian flavor symmetries such as $A_4$, whose triplet representation reduces free parameters to 4 at leading order, is required specifically for mixing structure. This obstruction applies to the well-motivated subclass of models where left-handed fields are uncharged; models that assign abelian charges to both left- and right-handed fields can evade it.

We identify universal signatures in the bispectrum arising from a transient tachyonic instability of entropic fluctuations during inflation, a phenomenon that naturally arises in hyperbolic field-space geometries. We perform exact numerical calculations directly at the level of fluctuations, without relying on a specific background model, and distinguish two cases. In the light case, with masses around the Hubble scale, our results provide the first-ever computation of the bispectrum due to such tachyonic instabilities. We find a universal magnification of the folded configuration, together with the known non-analytic scaling in the squeezed limit. As an illustrative example, we compute and analyse the bispectrum in angular inflation, demonstrating compatibility with current limits. In the heavy case, with masses well above the Hubble scale, the bispectrum exhibits a distinctive correlation between magnified folded configurations and a `tachyonic resonance' in mildly squeezed limits, with the resonance scale set by the strength of the instability. While the main qualitative features are reproduced, we show that there exists no UV matching for which a single-field effective description, obtained by integrating out the entropic modes, accurately captures the bispectrum for all kinematic configurations. To facilitate observational applications, we introduce simple bispectrum shape templates suitable for current and forthcoming cosmological surveys. Our model-independent results allow for constraining non-standard inflationary attractors characterised by strongly non-geodesic motion.

We construct toral Chern-Simons theory with gauge group $\mathbb T=\mathfrak t/\Lambda\cong U(1)^n$ from an even, integral, nondegenerate symmetric bilinear form $K:\Lambda\times\Lambda\to\mathbb Z$ by geometric quantization via real polarization. We obtain a unitary extended $(2+1)$-dimensional TQFT by constructing the boundary state spaces and canonical operators and proving that they satisfy the cylinder and gluing axioms. The finite discriminant group $G_K=\Lambda^*/K\Lambda$ arises naturally in the theory and controls the genus-$g$ state spaces. At genus one, the theory recovers the finite quadratic data underlying bosonic Abelian topological order.

We study excited solutions in a Skyrme–Chern-Simons theory in $2+1$ dimensions. In particular, we emphasize the necessity of using a Lagrange multiplier method to obtain excited solutions, due to the appearance of a discontinuity when using a constraint compliant parametrization. These solutions are characterized by an integer number $p$, excited solutions corresponding to $p\neq 0$. The dependence of the global charges on the parameters is analyzed, showing non-standard behaviors. We also find that the presence of the Skyrme–Chern-Simons term does not alter significantly the pattern of energy levels, so $p=0$ solutions (fundamental solutions) have always the minimal energy.

We calculate the one-loop renormalization group equations of the neutrino mass matrix when the Standard Model particle content is extended with a massive gauge boson which has family-dependent couplings to the left-handed leptons. We show that quantum effects induced by the extra gauge boson increase the rank of the neutrino mass matrix at the one-loop level, in contrast to the well-known result that Standard Model fields can only increase the rank at the two-loop level. We also discuss the possibility of generating dynamically the measured mass differences and mixing angles between the active neutrinos in scenarios with normal and inverted mass ordering.

We construct a family of exactly solvable relativistic kinetic theories in $1+1$ dimensions whose hydrodynamic sector continuously interpolates between Fick's and Cattaneo's laws of diffusion. The interpolation is controlled by a single parameter $a\in[0,1]$, which tunes the microscopic scattering dynamics from infinitely soft but infinitely frequent scatterings ($a=0$), reproducing standard diffusion, to maximally hard but finite-rate scatterings ($a=1$), yielding hyperbolic Cattaneo-type transport. For intermediate values of $a$, the dynamics combines frequent weak scatterings with rare strong randomizing events, providing a concrete microscopic realization of mixed diffusive-telegraphic behavior. Remarkably, the full quasinormal mode spectrum can be obtained analytically for all $a$. This allows us to track explicitly how purely diffusive modes continuously deform into damped propagating modes as the collision structure is varied.

The $p$-adic string worldsheet action on the quotient of the Bruhat-Tits tree of $PGL(2,\mathbb{Q}_p)$ by a genus 1 Schottky group has a dual description on the asymptotic boundary, the Tate curve $\mathbb{Q}_p^\ast/q^\mathbb{Z}$. We show that the two point function of the dual action coincides with the Néron-Tate local height function of the Tate curve.

We investigate the dynamical stability and phase transition behavior in a holographic superfluid model incorporating higher-order self-interaction terms $\lambda |\psi|^4$, $\tau|\psi|^6$, and a non-minimal coupling $h(\psi)=e^{\alpha|\psi|^2}$. Thermodynamic and dynamical stability analyzes show that the thermodynamic stability and dynamical stability of the system are consistent. Phase diagram analysis reveals rich critical and supercritical phenomena. For fixed $\lambda<0$ and $\alpha$, increasing $\tau$ shrinks the first-order phase transition region to a critical point and then enters the supercritical region. When varying $\alpha$, the system can exhibit no critical point and, most notably, a double critical phenomenon in which, as $\alpha$ increases, the system first enters the supercritical region and then re-enters the first-order phase transition region. This double critical phenomenon driven by a single parameter is reported for the first time in holographic superfluid models, revealing a complex nonmonotonic coupling effect between the non-minimal coupling and higher-order interaction terms.

We establish a connection between the superconformal index of $\mathcal{N}=4$ $U(N)$ SYM and the elliptic Ruijsenaars-Schneider integrable system. The index admits an expression in terms of elliptic Macdonald polynomials, which leads to a compact summation over generalized partitions involving the structure constants $B_\lambda(p,q,t)$ and normalization constants $\mathcal{N}_\lambda(p,q,t)$. By solving the elliptic Ruijsenaars-Schneider model perturbatively in the elliptic parameter $p$, a systematic expansion of the index in powers of $p$ is obtained. We check that in various limits, namely a deformed 1/2 BPS limit and especially the large $N$ limit, our formalism reduces to previously known results.

We construct and analyze a class of one-dimensional boundary Hamiltonians arising from two-dimensional symmetry-protected topological phases with $\mathbb{Z}_N^{\times 3}$ symmetry on a triangular lattice. Using a cohomology-based transformation, the lattice models for the edge modes are explicitly obtained, and their structure is shown to be governed by the arithmetic properties of $N$. For prime $N$, the boundary theory admits a formulation in terms of mutually commuting Temperley-Lieb algebras. For the composite values of $N$, the models exhibit hierarchical or factorized structures. We demonstrate that the phases can be understood in terms of primary models augmented by local defect degrees of freedom that partition the system into independent segments. Finally, the global symmetry is realized on the boundary in a non-on-site and anomalous manner, directly realizing the corresponding 't Hooft anomaly.

In this paper, we perform a detailed study of the thermodynamic properties of a charged black hole in bumblebee gravity in the presence of a global monopole. We also analyze the optical characteristics of this black hole solution, highlighting the influence of Lorentz symmetry violation and the global monopole on the black hole shadow. Furthermore, we examine the trajectories of both photons and test particles in this spacetime, showing how the geometric parameters alter their paths. Moreover, we study the dynamics of neutral test particles, with particular attention to the location of the innermost stable circular orbits (ISCOs). Finally, we investigate massless scalar perturbations and derive bounds on the greybody factors, illustrating how the black hole's geometric parameters affect field propagation, energy emission, and radiation sparsity in this background.

A folklore conjecture states that the Nahm sum associated with a pair of Dynkin diagrams of type $ADET$ is a modular function. In this paper, we extend this conjecture to Dynkin diagrams of type $ABCDEFGT$ in the context of generalized Nahm sums. The modular Nahm sums are closely related to the characters of 2d rational conformal field theories. In this work, we identify many specific generalized Nahm sums with characters of some well-studied 2d CFTs. For example, we find that the generalized Nahm sums associated with $(T_1, C_r)$ and $(T_1,D_r)$ correspond to the supersymmetric Virasoro minimal models $\mathrm{SM}(4r+6, 4)$ and $\mathrm{SM}(8r+4, 2)$, respectively.

We show that an impurity quasiparticle immersed in a Bose-Einstein condensate, known as a Bose polaron, exhibits topological properties characterized by a nonzero Berry curvature, which is induced by Weyl nodes that emerge via interspecies $p$-wave Feshbach resonance. Such nodes occur even in the absence of spin degrees of freedom and spin-orbit coupling. For charged impurities, the corresponding $p$-wave polarons are shown to be accompanied by chiral anomaly. The above predictions can be tested in a cold atomic environment by observing the Hall transport of the atomic or ionic impurity cloud.

We discuss a Wakimoto-like free field realisation of ${\frak d}(2,1;\alpha)_1$, whose $\frak{sl}(2,\mathbb{R})$ subalgebra has level $k=1$, that requires no gauging, i.e., realises the current algebra exactly. We then compute the partition function of the theory and show that, by combining this with the ghost contribution, the full, on-shell projected string partition function reproduces precisely the single-particle partition function of the ${\rm Sym}^N({\cal S'}_0^2)$ theory, i.e. the symmetric orbifold theory of 8 free fermions, 1 compact free boson, and 1 non-compact free boson. We also discuss other aspects such as DDF operators and BRST and physical state conditions.

We construct static black hole solutions coexisting with anisotropic matter in asymptotically (anti-)de Sitter spacetime and investigate how the matter field modifies their thermodynamic and dynamical properties. The anisotropic matter generates an exponentially decaying charge-like contribution to the metric, causing the geometry to interpolate between the Schwarzschild black hole in anti-de Sitter spacetime and the Reissner-Nordström black hole in anti-de Sitter spacetime. In anti-de Sitter black hole spacetime, we derive the complete thermodynamic description, including the Hawking temperature, heat capacity, Smarr relation, generalized first law, and Helmholtz free energy. The system exhibits a van der Waals-type small/large black hole phase transition with a critical point determined by the matter field parameters. Local thermodynamic stability is characterized by the heat capacity, whereas global stability is determined through the free energy. We further investigate unstable homoclinic orbits by evaluating the Lyapunov exponent associated with null geodesics. Our analysis reveals that different thermodynamic branches possess distinct dynamical instabilities, and that the thermodynamically preferred phase is accompanied by a smaller Lyapunov exponent. These results demonstrate that thermodynamic stability and geodesic instability are correlated because both originate from the same underlying spacetime geometry.

We investigate the coupled dynamics of symmetry breaking and phase separation during quenches across the critical point in a first-order phase transition. Based on the Einstein-Maxwell-scalar theory, we construct a holographic superfluid model with $\mathbb{Z}_2$ symmetry. By introducing higher-order nonlinear terms $\lambda\Psi^4$ and $\tau\Psi^6$ into the scalar field potential, we realize a rich phase structure, which enables us to study the coupling effects between symmetry breaking and phase separation. Furthermore, by preparing initial conditions with well-defined spatial partitions, we discover a new triggering mechanism for the invasion phenomenon, namely that kinks serve as triggering sites for the phase separation process. This study reveals a novel coupling mechanism between topological defects and phase separation, enriches our understanding of nonequilibrium structure formation in strongly coupled systems.

The IKKT matrix model arises at the extremal $p= -1$ limit of holographic dualities based on D$p$-brane geometries. We review the one-dimensional maximal supergravity that governs bulk fluctuations dual to the lowest BPS multiplet of gauge-invariant operators in the IKKT model. We present the Killing spinor equations and discuss their general half-supersymmetric solutions within the $\rm{SO}(3)\times \rm{SO}(7)$-invariant subsector. The explicit uplift of these solutions to Euclidean IIB supergravity in ten dimensions is provided.

Lieb-Schultz-Mattis (LSM) anomalies are powerful symmetry-based constraints on the correlation, entanglement and dynamics of quantum many-body systems. In this review, we discuss various LSM anomalies and anomaly matching. We start with a pedagogical introduction to these subjects in quantum spin chains, and then generalize the discussion to higher dimensions and other systems. Besides covering the topics related to the standard LSM anomalies, we also review LSM anomalies in disordered systems where the lattice symmetries are only preserved on average, fermionic systems, and systems where the symmetric short-range entangled states are possible but must be nontrivial symmetry-protected topological phases.