Papers

The mass spectrum of pseudoscalar and scalar meson modes at finite temperature is studied in the framework of a nonlocal quark model. The model implements quark confinement via the modification of the Laplace transform of the quark propagator. In order to synchronize the confining and deconfining phases, a modification of the transform is proposed. The behavior of the screening masses of mesons is studied in a wide region of temperatures, while the pole masses are described up to the deconfining phase transition.

This study demonstrates that the common practice of determining spontaneous Lorentz violation via the minimum of a Lagrangian potential is generally incorrect. By analyzing the Hamiltonian structure and constraints of vector fields, we show that the true vacuum must be derived from the Hamiltonian density. We prove that the standard quadratic potential cannot consistently generate a vacuum expectation value (VEV), identifying a cubic potential as the simplest viable alternative. Furthermore, we prove that smooth potentials only support stable timelike or lightlike VEVs. These conclusions extend to higher-rank tensor fields and impose rigorous consistency constraints on higher-rank tensor fields and Lorentz-violating effective field theories.

Is gauge symmetry merely a redundancy in our description, or does it carry a deeper information-theoretic significance? Quantum error-correcting codes (QECCs) show that redundancy can serve as a resource for protecting information against noise. In this work, we ask whether gauge theories can be understood in similar terms, and make this idea concrete in lattice quantum electrodynamics (QED), building on and extending earlier works that established a bridge between gauge systems, stabilizer codes, and quantum reference frames (QRFs). For Abelian gauge groups, we show that explicit recovery operations can be constructed using group-theoretical methods for error sets determined by both ideal and non-ideal QRFs. Applied to lattice QED, this yields two QECC structures: one in the pure-gauge sector and one including fermions. We construct a gauge-field QRF based on spanning trees of the lattice and a fermionic field QRF from the matter field, thereby making explicit how physical information is encoded. While the syndromes of gauge-violating errors associated with constraint measurements are generically degenerate, QRFs resolve this degeneracy and single out families of correctable errors. This establishes lattice QED as a QECC beyond the stabilizer setting and shows concretely how gauge symmetry provides an encoding structure that supports error correction.

We study the inflationary bispectrum generated by the tree-level exchange of a massive hidden-sector scalar during inflation. When the interaction between the inflaton and the hidden sector arises only from the leading boost-breaking operator of the Effective Field Theory (EFT) of inflation, the equilateral bispectrum for principal-series scalar exchange is known to be universally negative, independent of the sign of the coupling. We revisit this result within the full EFT operator basis. Using bootstrap methods, we construct the de Sitter-invariant seed four-point function and obtain the inflationary bispectrum via weight-shifting operators and a soft-limit procedure. While the equilateral bispectrum remains strictly negative when only the leading interaction is present, additional operators generate independent cubic structures whose contributions compete in the equilateral configuration. As a result, the sign of the bispectrum is no longer universal. We derive a critical ratio of interaction coefficients that separates regions of positive and negative equilateral bispectrum. We further study the effects of reduced sound speed $c_s<1$ and the exchange of multiple particles. In both cases, the critical ratio is modified, and for multi-particle exchange a positive equilateral bispectrum can arise even when the higher-order operator is subdominant. Our results show that the negativity of the equilateral bispectrum from massive exchange is not generic, but reflects a restricted operator structure in the EFT of inflation.

In this work, we investigate the effects of Lorentz symmetry violation on the absorption cross section and quasinormal modes of a rotating acoustic black hole in (2+1) dimensions, within the regime of slow rotation and small Lorentz violating parameter $\alpha$. The absorption cross section was analyzed analytically, using the low and high frequency regimes, and numerically, through integration of the radial equation. The results showed that, in this regime, Lorentz violation increases the absorption cross section at all energy scales, with a contribution from the rotation parameter $B$ appearing even in the low frequency regime. For the quasinormal modes, we observed that symmetry breaking decreases the real part of the frequencies and increases the magnitude of the corresponding imaginary part, indicating a faster damping of the oscillations.

We provide a relatively self-contained introduction to the application of quantum spacetime and quantum Riemannian geometry to theoretical physics. Recent successes include calculation of the vacuum energy of spacetime curvature fluctuations in a single-plaquette model of quantum gravity, derivation of the Kaluza-Klein ansatz as a consequence of quantum spacetime, exactly conserved Noether charges from variational calculus on a lattice, and a new theory of classical and quantum geodesics. The latter leads to a theory of generally covariant quantum mechanics applicable in General Relativity with intriguing first results for the case of a black-hole. We discuss several open problems past and present, and how they might be addressed going forward. New results include a phase transition for Euclidean quantum gravity on a 4-pointed star.

We study the relation between emergent 1-form symmetries and soft photon theorems in QED. We show that in the relevant massive and massless kinematic regimes, described respectively by HQET and SCET, the soft sector admits electric and magnetic 1-form symmetries. We then show that these symmetries give rise to an infinite-dimensional Abelian algebra of ordinary conserved charges, with a central extension. In Minkowski spacetime, suitable choices of hypersurfaces reduce these charges to the familiar asymptotic symmetry charges and imply the leading electric and magnetic soft photon theorems. We further show that the central term in this algebra fixes a contact term appearing in scattering amplitudes involving two soft photons with mixed electric-magnetic polarizations. Finally, we extend the same construction to inclusive observables and apply it to QED photon detectors.

We develop a comprehensive framework for constructing quantum error correcting codes (QECCs) from Abelian lattice gauge theories (LGTs) using quantum reference frames (QRFs) as a unifying formalism. We consider LGTs with arbitrary compact Abelian gauge groups supported on lattices in arbitrary numbers of spatial dimensions, and we work with both pure gauge theories and theories with couplings to bosonic and fermionic matter. The codes that we construct fall into two classes: First, Gauss law codes identify the code subspace with the full gauge-invariant sector of the theory. In models with matter coupled to gauge fields, these codes inherit a natural subsystem structure in which gauge-invariant Wilson loops and dressed matter excitations factorize the code space. Second, vacuum codes restrict the code subspace to the matter vacuum sector within the gauge-invariant subspace, yielding codes where errors correspond to gauge-invariant charge excitations rather than to violations of the Gauss law. Despite their distinct setup, we show that when the gauge group is finite, vacuum codes are unitarily equivalent to pure gauge theory Gauss law codes, and that when the group is continuous, this is only true upon a charge coarse-graining of the vacuum code. In all cases, QRFs provide a systematic apparatus for fully characterizing the codes' algebraic structures and correctable error sets. For clarity, we illustrate our general results in $\mathbb{Z}_2$-gauge theory, as well as in scalar and fermionic QED. These findings offer fundamental insights into the parallelism between quantum error correction and gauge theory and point toward practical advantages for simulating LGTs on noisy quantum devices.

In this paper, we investigate the long range gravitational effect of curvature-scalar field non-minimal coupling in the form of $\xi R \phi^2$, in the perturbative quantum gravity framework. Such coupling is most naturally motivated from the renormalisation of a scalar field theory with a quartic self interaction in a curved spacetime background. This coupling results in two scalar-$n$ graviton vertices which contain no explicit momenta of the scalar, qualitatively different from the usual, e.g., $\kappa h^{\mu\nu}T_{\mu\nu}$-type minimal matter-graviton vertices. Assuming the dimensionless coupling parameter $\xi$ to be small, we compute the 2-2 scattering Feynman amplitudes between such scalars up to ${\cal O}(G^2 \xi)$. From the non-relativistic limit of these amplitudes, we compute the corresponding long range gravitational potential. There exists no tree level contribution $({\cal O}(\xi G))$ here, and hence the one loop ${\cal O}(G^2 \xi)$ result is leading. Recently, the effect of a cosmological constant in such non-minimal interaction and the subsequent gravitational potential was computed. In this work, we take the cosmological constant to be vanishing. The resulting potential is found to have $r^{-4}$ leading behavior. We further extend these results for scalar-massive spin-1 and massive spin-1/2 scattering. Spin and polarisation dependence of the two body potential have been explicitly demonstrated. We discuss some possible physical implications of these results.

This note reports the following observation: the finite-volume expectation value of the spin operator (the one-point function) between the $\mathbb{Z}_2$-even and odd ground states in the critical periodic Ising chain, when continued as a complex-analytic function of the system length $N$ through the Borel resummation of its large-$N$ expansion, has a natural boundary of analyticity along the negative real axis. The singular behavior near the negative real axis, after an exponential map, is the same as that of a Lambert-type series for the odd-divisor-squared sum near the unit circle $|z|=1$. The same divisor sum also governs the strengths of the Borel discontinuities of the one-point function's factorially-divergent large-$N$ asymptotics. We also report the all-order large-$N$ asymptotics of the leg function for the finite-volume spin-operator form factor, and the similarities to certain known quantities in the literature.

Gravitational waves provide a unique probe of the strong-field regime of gravity, offering access to physics beyond the classical black hole paradigm. We explore how space-based observations of extreme-mass-ratio inspirals (EMRIs) by the Laser Interferometer Space Antenna (LISA) can be used to test for departures from the Kerr geometry, and in particular for the breaking of its axial and equatorial symmetries, as expected in quantum-gravity-inspired alternatives to Kerr black holes such as the fuzzball proposal. By introducing generic multipolar deformations encoding potential symmetry breakings and performing a systematic parameter estimation analysis, we forecast LISA's ability to constrain such departures from the Kerr geometry in the strong-field regime. We show that EMRI signals with realistic signal-to-noise ratios can constrain several higher-order multipoles of the primary, opening a new observational window onto strong-field deviations from the Kerr geometry. In particular, we find that LISA can constrain generic nonaxisymmetric mass quadrupole deformations at the $10^{-4}-10^{-2}$ level and axisymmetric mass octupole deformations at the $10^{-1}$-$10^{0}$ level, providing concrete observational targets for strong-field deviations from the Kerr geometry, such as those that may arise in fuzzball and other exotic-compact-object scenarios. Our results demonstrate that precision measurements of EMRI waveforms will transform LISA into a powerful laboratory for fundamental physics and offer precise constraints on quantum-gravity-motivated models of compact objects.

We investigate the quasinormal modes (QNMs) associated with intrinsic metric-dilaton coupled perturbations of the Mandal-Sengupta-Wadia (MSW) black hole in two-dimensional string theory. Through suitable field redefinitions, the gravity-dilaton system is expressed in terms of the conformal factor and a redefined dilaton field, allowing the linear perturbation equations to be reduced to coupled Schrodinger-type eigenvalue equations in the tortoise coordinate. By imposing the standard QNMs' boundary conditions of purely ingoing waves at the horizon and purely outgoing waves at spatial infinity, we numerically determine the complex frequency spectrum. All modes satisfy Im$(\omega)<0$, confirming the linear stability of the MSW black hole under intrinsic coupled perturbations. Unlike external scalar-field perturbations, which yield purely imaginary frequencies, the intrinsic perturbations generically exhibit nonvanishing real parts, corresponding to oscillatory modes of the gravity-dilaton sector. The real part of the frequency displays a nonmonotonic dependence on the overtone number, while increasing the central-charge parameter $\sqrt{k}$ systematically decreases the damping rate and prolongs the relaxation time. These results indicate that intrinsic perturbations probe internal dynamical degrees of freedom and reveal characteristic features of the relaxation dynamics of two-dimensional stringy black holes.

We introduce a new method that exploits the combination of the Heat Kernel (HK) and Background Field Method to compute gauge-invariant and gauge parameter-independent quantities such as the effective potential, anomalous dimensions, and renormalization group equations. In contrast to currently employed techniques, these results are obtained exclusively from the dynamics of the background fields, without relying on supplementary input from, e.g., traditional diagrammatic calculations. This is achieved by a consistent treatment of open and closed derivatives in the HK expansions. In this way, we compute the standard quantities such as $\beta$ functions and their gauge-parameter independence when background fields are on-shell. We demonstrate this formalism for instructive examples such as Scalar QED and Yukawa theory. Full results for the bosonic part of the Standard Model provide further validation of our approach.

We apply artificial neural networks to the holographic inverse problem, reconstructing bulk geometry from boundary entanglement entropy by using the Ryu–Takayanagi area functional as a differentiable loss. Validated on the AdS-Schwarzschild background, this approach recovers the blackening factor with maximum absolute error below $3\times10^{-3}$ across the entire bulk, reproducibly over independent training runs. For finite-density backgrounds like the Gubser–Rocha model, we demonstrate that equal-time strip entanglement entropy determines only the spatial metric. We resolve this exact one-function degeneracy by incorporating holographic Wilson loop data, which couples to the timelike metric. We present a semi-analytical inversion combining Bilson's and Hashimoto's formulas, alongside a general three-network variational method minimizing the combined area and Nambu–Goto actions. The neural network achieves maximum relative errors below $0.2\%$ for both metric functions without closed-form derivative relations, and accommodates additional holographic observables at the cost of one extra network and loss term.

Previously, we proposed an infrared vacuum wave functional for $SU(N)$ Yang-Mills theory peaked at thin center vortices and showed that it yields an area law for the Wilson loop. In this work, we use this wave functional to calculate the spatial 't Hooft loop, for which we find a perimeter law, in accordance with 't Hooft's criterion for confinement.

We calculate the resummed perturbative free energy of ${\cal N} = 4$ supersymmetric Yang-Mills in four spacetime dimensions (SYM$_{44}$) to order $\lambda^{5/2}$ in the 't Hooft coupling at finite temperature and zero chemical potential. All infrared divergences cancel when we include contributions from SYM$_{44}$ ring diagrams and the final result is both ultraviolet and infrared finite. Our result has special significance since order $\lambda^{5/2}$ is the highest order calculation that can be done with perturbation theory, because there are nonperturbative effects associated with the magnetic mass scale that come into play at order $\lambda^3$. We compare results obtained with regularization by dimensional reduction (RDR), which preserves supersymmetry, and canonical dimensional regularization (DR). We also compare with a generalized Padé approximant constructed by matching the weak coupling result at order $\lambda^2$ and the large $N_c$ strong coupling result at order $\lambda^{-3/2}$. Finally we make a comparison between our result and the QCD free energy and show that SYM$_{44}$ has better convergence properties.

Localized one-particle states of a quantum field theory–whether in flat space or on a curved background–are expected to exhibit geodesic motion in an appropriate semiclassical regime. This expectation is often invoked heuristically: in this work we develop two precise implementations and test them in detail in global AdS$_3$. First, we define a covariant ”center-of-mass” trajectory from the expectation value of the stress tensor operator and show, using only $\nabla_\mu\langle T^{\mu\nu}\rangle=0$, that it obeys the geodesic equation in the monopole (sufficiently localized) approximation in a general spacetime. This provides a QFT-in-curved-spacetime generalization of the Mathisson-Papapetrou-Dixon framework in classical general relativity. Second, we construct position operators from the Klein–Gordon inner product and mode completeness, and compute their expectation values in generic single-particle wave packet states. We then build explicit normalizable wave packets of a free scalar field in empty AdS$_3$ with tunable energy and angular momentum, and demonstrate analytically and numerically that both prescriptions reproduce the expected radial, circular, and elliptical-like timelike and null geodesics. Our discussion also isolates a natural ultra-relativistic regime in which the wave packet trajectory exhibits a controlled crossover from timelike to null geodesic behavior. We identify precise limits where the localized geodesic interpretation of the wave packet breaks down. On the CFT side, we show that bulk localization–specifically the radial data–is captured by how the state is distributed over global descendants of the dual primary.

We investigate abelian Chern-Simons gauge theory on a strip geometry with two spatial boundaries. In the presence of boundaries, gauge invariance is broken by boundary conditions, leading to physical edge excitations. By deriving the most general local boundary conditions consistent with power counting in the sense of Symanzik, we show that the bulk equations of motion determine the boundary degrees of freedom through a broken gauge Ward identity, yielding boundary Kac-Moody current algebras with opposite central charges on the two edges. The corresponding two-dimensional boundary actions are of Tomonaga-Luttinger type and describe chiral bosons propagating in opposite directions along the two boundaries. A consistency condition, interpreted as a holographic-like bulk-boundary matching, relates the Chern-Simons coupling constant and the boundary parameters to the physical edge velocities. Within this framework, the equality and opposite sign of the two velocities in a symmetric setup follow directly from the boundary structure rather than from model-dependent assumptions about confining potentials, and the velocities are independent of the strip width. Our analysis provides a fully field-theoretic realization of bulk-boundary correspondence in Chern-Simons theory with two boundaries, with direct applications to edge physics in quantum Hall systems and related topological/hydrodynamic settings.

We study non-Hermitian quantum mechanics of an inverted triple-well potential within the exact WKB framework. For a single classical potential, different Siegert boundary conditions define three distinct quantum problems: the PT-symmetric, resonance, and anti-resonance systems. For each case, we derive the exact quantization condition and construct the associated trans-series solution. By identifying the resurgent structures and cancellations in these non-Hermitian setups, we obtain the median-summed series, clarifying when the spectra are real or complex in accordance with the physical properties of each system. Establishing explicit links to the semi-classical path integral formalism, we elucidate the roles of bounce and bion configurations in these non-Hermitian systems. This analysis predicts PT-symmetry breaking, which we also verify numerically. Using the median quantization conditions, we prove the existence of this symmetry breaking and establish an exact equation for the exceptional point, which emerges as a remarkably simple algebraic relation between the bounce and bion actions. We further show that the median-summed non-perturbative correction to the spectrum vanishes at the exceptional point, while the resurgent structure survives through a universal minimal trans-series. For the resonance and anti-resonance systems, we find that the exact median-summed spectra are related by complex conjugation, representing time reversal in this setting, are necessarily complex, and do not exhibit an exceptional point. Although their spectra differ significantly from the PT-symmetric case, they share the same minimal trans-series. By maintaining explicit links with the path integral saddles and the formal theory of resurgence, our analysis provides a unified and general perspective on the quantization of non-Hermitian theories.

Black hole islands are usually diagnosed through the von Neumann entropy, but the full replica saddle contains more information than survives in the limit $n \to 1$. In this paper we show that the capacity of entanglement can detect that extra structure already within the controlled factorized island branch of JT gravity coupled to a large-$c$ bath. In the late-time high-temperature regime, the entropy plateau remains unchanged at the first nontrivial order, while the capacity acquires a definite correction. This provides a sharp semiclassical example in which nearby replica data are physically meaningful even when the entropy itself appears rigid. Our result shows that the factorized island saddle already carries finite-$n$ information beyond the entropy, and that the capacity is a natural observable for exposing it. More broadly, it highlights that the physics of island saddles is not exhausted by the $n=1$ limit: the surrounding replica geometry can contain additional, and observable, information about how the semiclassical saddle is assembled.

The quantum Rabi model has been a useful and pedagogical quantum model in the past decades, sufficiently simple to be solved analytically and intuitively understood, while sufficiently complex as to provide highly non-trivial eigenstates and a practical description of quantum optical platforms for quantum technologies. The Dirac equation, especially when restricted to 1+1 dimensions, is a simple toy model as well, but its easy diagonalization enabled historically to connect the electron spin to the fermionic statistics, among others. Both models share a symmetry at the purely mathematical level, namely, the spectra of each one has a dual equivalent under energy sign change, that I name a mirror dual symmetry. Usually, one quantizes these equations by assuming a ground state energy for the bosonic mode. But there is another option for the interpretation of the Hamiltonian, as I will argue, that is to assume a total symmetry principle, namely, that the total energy is zero at all times, for either the quantum Rabi model or the Dirac equation, and impose the constraint that every positive energy excitation has a mirror excitation of negative energy. This possibility, which was, apparently, ignored in the times when Paul Dirac was studying the implications of his equation, would avoid the worries in the scientific community that the negative energy solutions would decay until minus infinity, thus obviating the necessity to build a highly artificial Dirac sea, and instead impose what has always been successful in Physics, which is the enforcement of symmetry principles. Assuming a total symmetry principle, many of the problems of current Physics, such as renormalization of quantum gravity, dark matter, and dark energy, may possibly be automatically solved. One obvious result would be the automatic cancellation of the zero point energy.

We study solution-generating techniques based on the Breitenlohner–Maison linear system for extremal, stationary biaxisymmetric black hole solutions in five-dimensional $U(1)^3$ supergravity. Focusing on multi-center configurations over a Gibbons–Hawking base, we analyze both BPS and almost-BPS solutions, including rotating single-center black holes and two-center black rings. After dimensional reduction to three dimensions, the system is described by a coset sigma model with target space $SO(4,4)/[SO(2,2)\times SO(2,2)]$, where solutions are encoded in coset and monodromy matrices. For Bena–Warner BPS solutions, we construct the coset and monodromy matrices and show that they admit an exponential representation governed by nilpotent elements. Although the monodromy matrices generically exhibit double poles, they can be factorized explicitly using the nilpotent algebra of $\mathfrak{so}(4,4)$, reconstructing the solutions. We extend this to almost-BPS solutions and derive the corresponding matrices. While the single-center case exhibits commuting residues, the two-center black ring leads to a more intricate structure with a third-order pole, which disappears when regularity is imposed. Finally, we analyze the extremal limits of the Rasheed–Larsen solution, where the fast-rotating branch is governed by idempotent elements. We also construct an explicit $SO(4,4)$ duality transformation relating the slowly-rotating branch to a single-center almost-BPS solution. These results will provide the BM formalism as a unified framework for extremal multi-center black holes.

We establish a correspondence between vortex equations on flat Riemann surfaces and harmonic spinors on the Nappi–Witten space, the group manifold of a central extension of the Euclidean group $SE(2)$. Vortex configurations lift naturally to this setting, producing explicit solutions of a twisted Dirac equation. Using the conformal flatness of the Nappi–Witten metric, these solutions induce harmonic spinors on four-dimensional Minkowski space. This yields a geometric construction of Abelian magnetic zero-modes on flat Minkowski spacetime from vortex data.

This paper investigates phantom BTZ black holes within the high-curvature gravity theory framework, specifically using a special case of power-Maxwell theory, which functions as a nonlinear electrodynamics source called F(R)-conformally invariant Maxwell gravity. We examine how the phantom or anti-Maxwell field affects the structure of these black holes and how the theory's parameters influence their horizon structure. Additionally, we derive the conserved and thermodynamic potentials associated with these black holes, thereby establishing their conformance to the foundational first law of thermodynamics. Next, the stability characteristics of BTZ black holes endowed with phantom and Maxwell fields are explored under canonical and grand canonical ensemble conditions by inspecting their heat capacity and Gibbs free energy profiles. This assessment reveals how the phantom field and scalar curvature affect these stability regions. We then perform a rigorous analytical verification of the Ehrenfest equations to determine whether the critical behavior of the phantom BTZ black hole corresponds to a second-order phase transition. Our results demonstrate adherence to both Ehrenfest relations, thereby confirming the occurrence of a second-order phase transition within the black hole system concurrent with the critical point. Furthermore, we explore the geodesic structure of the obtained solutions to analyze the motion of massive and massless test particles in the $F(R)$-phantom BTZ spacetime. The analysis demonstrates that stable timelike circular orbits exist only in the phantom regime for negative curvature backgrounds, while the phantom configuration also allows for stable circular photon orbits. These results underscore the significant influence of the phantom field and the F(R) correction on the spacetime geometry and orbital dynamics.

Causal Dynamical Triangulations (CDT) is a methodology to define and compute the gravitational path integral, whose aim is a fully fledged nonperturbative quantum field theory of gravity and spacetime. Analogous to lattice formulations of nongravitational quantum fields, CDT provides a blueprint for lattice quantum gravity, where - crucially - the dynamical, curved and causal nature of spacetime is built into the structure of the lattices from the outset. The regularized path integral involves a sum over triangulated spacetimes, each assembled from flat, Minkowskian building blocks. The degrees of freedom of general relativity are encoded in a coordinate-free manner in the neighbourhood relations of the building blocks and the length of their edges, which also serves as a short-distance cutoff. A well-defined Wick rotation makes this path integral amenable to Monte Carlo simulations. Despite the absence of an a priori preferred background geometry, numerical experiments have revealed the dynamical emergence of a quantum universe near the Planck scale. Its global properties are compatible with those of a de Sitter space, providing strong evidence for a well-defined classical limit. At the same time, large quantum fluctuations lead to unexpected properties on short scales, most prominently, a spectral dimension near 2, replacing the classical value of 4. Computer simulations indicate the presence of an ultraviolet fixed point under renormalization, opening the door to a nontrivial continuum theory. Efforts are under way to construct observables that can elucidate the nonperturbative quantum origins of early-universe cosmology.

The symmetry-resolved Krylov complexity is a useful tool for studying the chaotic properties of systems endowed with symmetries. We investigate the conditions under which an invariant Hermitian operator would have the symmetry-resolved Krylov complexity in a charge subspace identical to the Krylov complexity of the full operator, and find a necessary and sufficient condition that ensures this matching at all temperatures. Further, we study the Krylov complexity of the Uncoloured Tensor Model, a disorder-free kin of the SYK Model, which has a plethora of symmetries. We identify charge subspaces of the same operator in which equipartition holds, as well as those where it doesn't, along with observations on the underlying mechanism behind these. We also find that, within the computational limits, the Krylov complexity, averaged over the symmetry subspace, is bounded above by that of the operator in the full space.

We consider a modular-invariant extension of the Standard Model. Assuming that the modulus is the inflaton, the CP-violating phases of the Yukawa couplings evolve during inflation. This dynamics favours a Higgs condensate, so that Standard Model fermions mediate a one-loop cosmological collider signal enhanced by chemical potentials. The effect appears too small for next-generation experiments. We provide precise expressions for Dirac fermions with chemical potentials in de Sitter.

We present a new family of Ricci-flat black hole and soliton solutions with primary scalar hair in asymptotically anti-de Sitter (AdS) space in $D$ dimensions. By solving the coupled Einstein-scalar field equations, we obtain analytic planar hairy black hole and soliton geometries. In these solutions, the scalar field and curvature scalars remain regular everywhere. We also derive analytic expressions for the mass and free energy, which indicate that the hairy soliton represents the ground state of the system. We further analyze the phase transitions between the hairy black hole and the hairy soliton, and find that there exists a first-order phase transition between them, with the transition point controlled by the ratio of the periods of Euclidean time and compact spacelike cycle. We further analyze how the scalar hair affects the transition temperature, and find that the temperature window in which the soliton phase remains preferred expands as the hair parameter increases. The hairy soliton solution obtained here is partly motivated by holographic QCD and may provide a useful gravitational background for modeling the confined phase of QCD from a bottom-up holographic perspective.

An interesting framework to achieve gauge coupling unification consists in adding to the Standard Model Lagrangian non-renormalizable operators of $d \geq 5$, which affect the kinetic term of gauge fields. We first review the phenomenology related to this framework in the context of $SU(5)$, identifying which are the most interesting representations for the sake of achieving coupling unification. Secondly, we point out that in the case of a dynamical breaking pattern, it is possible to relate gauge coupling unification with the doublet-triplet splitting problem. We show that condensates of fermions in the $5$ representation do not lead to viable models because of proton decay constraints. At difference, we point out that successful models can be obtained by considering condensates of fermions in the $10$, as well as in the $24$ representations.

We demonstrate a mechanism for the production of massive excitations in graphs. We treat the number of neighbors at each vertex in the graph (degree) as a scalar field. Then we introduce a mechanism inspired by the Higgs mechanism in quantum field theory(QFT), that couples the degree field to a vector-like field, introduced via the graph edges, represented mathematically by the incident matrices of the graph. The coupling between the two fields produces a massless ground state and massive excitations, separated by a mass gap. The excitations can be treated as emergent massive particles, propagating inside the graph. We study how the size of the graph and its density, represented by the ratio of edges over vertices, affects the mass gap and the localization properties of the massive excitations. We show that the most massive excitations, corresponding to the heaviest emergent particles, localize on regions of the graph with high density, consisting of vertices with a large degree. On the other hand, the least massive excitations, corresponding to the lightest emergent particles localize on a few vertices but with a smaller degree. Excitations with intermediate masses are less localized, spreading on more vertices instead. Our study shows that emergence of matter-like structures with various mass properties, is possible in discrete physical models, relying only on a few fundamental properties like the connectivity of the models.