Papers

Active feedback between geometry and physics is woven throughout the study of Nature at its fundamental level, and is of key importance in string theory. Methods of complex algebraic geometry in particular have brought about an unrivaled abundance of solutions, counted well into hundreds of orders of magnitude, reciprocated by the discovery of the wholly unexpected mirror symmetry. However, recent developments demonstrate that there are rich additional possibilities, made possible by certain generalizations that, at first glance, appear to be non-algebraic. Nevertheless, they are remarkably well-aligned within an overall mirror-symmetric framework, are amenable to almost as comprehensive quantitative analysis, and hint at a deeper relationship with symplectic geometry.

We observe a remarkable mathematical structure in the gap equations of the large-$N$ Gross–Neveu model at imaginary chemical potential in odd spacetime dimensions $d = 4k+3$. We show they can be written as the sum of two parts: one defined by higher-order discrete Laplacian patterns and a cut-off dependent part given by truncated asymptotic expansion of a hypergeometric function. We argue that this picture corresponds to a deeper relationship between thermal field theories in these odd $d$ and exactly-solvable one-dimensional quantum problems. We find that the thermal mass at specific imaginary chemical potential values is fixed where internal energy balances entropic states of thermal modes which is physically equivalent with OPE inversion formula techniques where thermal mass values arise from transcendental sets of equations.

We consider the ODE/IM correspondence for the value $c=-2$ of the Virasoro central charge (free-fermion point) and the associated quantum KdV model $-$ the quantization of the second hamiltonian structure of the classical periodic KdV model. We prove that the ODE/IM correspondence is complete (in the sense of V. Bazhanov, S. Lukyanov, and A. Zamolodchikov), namely that any solution of the Bethe equations coincides with the spectrum of a rational extension of the (quantum) harmonic oscillator. To this end, on the ODE side we consider Crum$-$Darboux transformations of the harmonic oscillator and the associated Laguerre Wronskians, which are remarkable special functions parametrized by pairs of partitions which we study in depth. As a further result, on the IM side, we diagonalize explicitly the first three hamiltonian operators of quantum KdV (in the free field representation): the eigenstates are Schur functions and the eigenvalues are shifted symmetric functions on partitions. We give two applications of this result: i) we prove that the eigenvalues are given by the evaluation of the Newton symmetric polynomials at the poles of the associated monster potentials, as further conjectured by V. Bazhanov, S. Lukyanov, and A. Zamolodchikov; ii) we show that these hamiltonian operators also belong to the algebra of hamiltonian operators obtained by quantizing the first hamiltonian structure of the classical periodic dispersionless KdV model.

We extend the perturbative null-surface formulation (NSF) scattering map to fourth order and derive an all-order recursion for the quantum cut. After the antipodal matching, both cone sources are evaluated on the same retarded solution determined by the free incoming radiative data. The perturbative NSF equations therefore determine every coefficient $Z_n$ from that data, without introducing new independent asymptotic information. The partial cut $Z_{[N]}=\sum_{j=1}^{N}\ep^j Z_j$ defines the cumulative operator $U_{\omega,[N]}=\exp[-\ii\omega Z_{[N]}]$. An exact factor recursion for this operator gives a generating formula for $\delta a_{n,\lambda}^{\mathrm{out}}$ in terms of the order-$n$ cone source and lower-order operators. The scalar flux term $\Sigma$, which begins quadratically, is included on the cut side of the matching equation; its free quadratic part cancels between future and past infinity and it never introduces a new order-$n$ radiative operator. For smooth smeared radiative data, every finite-order cut is well defined and self-adjoint, so $U_{\omega,[N]}$ and its recursive factors are unitary and bounded. The frequency powers in the perturbative coefficients are thus part of the expansion of a bounded unitary operator, rather than separate ultraviolet enhancements. At fourth order we formally determine $\delta a_{4,\lambda}^{\mathrm{out}}$ and identify the mixed one-loop sector $\mathcal M_{24}=\mathcal M^{(24)}+\mathcal M^{(42)}$. A general radial power-counting proposition proves ultraviolet finiteness at arbitrary perturbative order for the flat-cone two-vertex sectors. In particular, $\mathcal M_{24}$ and the previously obtained $\mathcal M_{33}$ both scale as $\int^\infty \dd K/K^4$ in the uniform radial ultraviolet region.

This study investigates the evaporation process of a Schwarzschild black hole, incorporating quantum corrections arising from conformal anomaly and vacuum polarization. We show that these quantum corrections significantly modify the Hawking radiation and thermodynamic behavior of the black hole. In particular, the Hawking temperature reaches a maximum value and subsequently decreases as the black hole loses mass, eventually vanishing in the extremal limit. The evaporation process therefore approaches an extremal remnant configuration with zero Hawking temperature. Furthermore, we demonstrate that the black hole entropy receives logarithmic corrections due to the modified thermodynamic structure. Hawking radiation is also analyzed using the Parikh-Wilczek tunneling method, which confirms the consistency of the obtained thermodynamic behavior within the quantum-corrected framework.

This work explores the quantum propagator $K(x,t)$ as a solution of the system's dynamical equation. We develop a generalized propagator framework in which the propagator is written in the form $K=\exp\!\left(R+\frac{i}{\hbar}S\right)$, where $S$ governs the semiclassical phase structure and $R$ governs the amplitude transport and weighting of configurations. Starting from nonrelativistic quantum mechanics, the classical Hamilton–Jacobi equation emerges in the semiclassical limit, while $R$ reduces to the logarithm of the Van Vleck determinant. The formalism is then extended to relativistic field theory and minisuperspace quantum cosmology using functional methods and generalized Hamiltonian constraints. Then the resulting semiclassical equations recover the corresponding classical dynamics along characteristic flows. In minisuperspace models, the formalism yields coupled equations for geometric and matter sectors analogous to semiclassical Wheeler–DeWitt systems. In semiclassical gravitational settings, the gravitational contribution may admit an entropy-like interpretation, consistent with thermodynamic weighting factors appearing in Euclidean gravitational path integrals. The resulting framework suggests a unified semiclassical description in which propagator phases encode dynamical evolution while amplitude functionals encode transport and configuration weighting. This perspective motivates viewing mechanics as a relation between the differential structure of spacetime and the differential structure of the space of dynamical configurations.

xCPS is an xAct tensor algebra package for symbolic computations within the covariant phase space formalism of field theories. From a generic Lagrangian, xCPS automates the derivation of equations of motion and symplectic currents. It systematically determines whether an infinitesimal transformation in the space of fields is a Noether symmetry and computes the associated Noether charge. Additionally, xCPS can in many cases determine whether a tensorial expression is a divergence and, if so, find its divergence potential. By implementing vertical exterior calculus through a graded, supercommutative wedge product and vertical operators, the package enables efficient computations in gauge theories and higher-derivative models of gravity, including the derivation of thermodynamic quantities like Wald's entropy. xCPS is open-source under the GPL license and available at https://github.com/juanmargalef.

We show explicitly that radiation from a uniformly accelerating charge escapes outside Rindler wedge, while within Rindler wedge there is no flux through infinity, neither in the Minkowski frame nor in the Rindler frame. This remains true despite the fact that the coordinate transformation between the Rindler and Minkowski frames is not trivial at infinity.

The genus-g Fuss–Catalan (FC) number counts the number of ways to obtain a genus-g surface by identifying the edges of a pn-gon via p-valent hyperedges. For p=2 these are the genus–g Catalan numbers which are generated as the trace correlations in the Gaussian matrix model (GUE). Here we construct a simple two-matrix model which generates the higher-genus Fuss-Catalan numbers for any p as the coefficients of its 1/N-expansion. We obtain exact sum rules and an explicit formula for the higher-genus Fuss–Catalan numbers which generalises the Harer–Zagier formula to p>2. We discuss the relation of the higher-genus FC numbers to the intersection numbers and the Euler characteristic of the moduli space of spin-p curves.

In the context of semiclassical gravity, the semiclassical Einstein equation is often invoked when backreaction of quantum matter/fields on the spacetime is at stake. It is expected to hold when quantum fluctuations are small. Yet, it is routinely used to justify the central role of the expectation value of the stress-energy tensor of quantum fields, whose fluctuations formally diverge. Here we propose a new way to probe the limits of this approximation by exploiting peculiar nonlinearities of gravity. As a proof of principle, we construct a controlled, analytically tractable setting where the incoherent mixture of weak-gravity states drives the system into a strong-gravity regime. By selecting a branch-degenerate observable, one can compare predictions of quantum and semiclassical gravity, potentially delimiting the validity of the latter.

We study the Bremsstrahlung function in two four-dimensional $\mathcal{N}=2$ superconformal gauge theories: the E-theory, with hypermultiplets in the symmetric and antisymmetric representations, and the D-theory, with antisymmetric and fundamental matter. Using matrix model techniques, we derive exact results at arbitrary coupling for the first few orders in the large-$N$ expansion. At leading order, both theories are shown to be planar equivalent to $\mathcal{N}=4$ Super Yang-Mills, while beyond the planar limit their behavior differs significantly. For the E-theory, we prove that the subleading correction is exactly given by a derivative of the free energy with respect to the coupling. This relation enables us to determine the complete strong-coupling expansion for the Bremsstrahlung function, including non-perturbative contributions, by exploiting known results for the free energy. For the D-theory, the exact expressions have a more intricate structure. We perform a detailed analysis of the strong-coupling regime of the subleading large-$N$ corrections, showing that, in this case, there are expansions in inverse powers of the coupling which truncate after finitely many terms. We further analyze the non-perturbative effects at strong coupling and derive closed-form expressions also for these contributions. These results provide precise predictions for the holographic duals of both theories beyond the supergravity approximation, probing higher orders in the large-$N$ expansion and the full subleading corrections at strong coupling.

This work investigates the semiclassical evolution of the Hawking atmosphere surrounding evaporating, spherically symmetric anti-de Sitter (adS) black holes. We model the evaporation process within a dynamical framework, treating the emission of Hawking radiation as a quantum tunneling process through the black-hole horizon. Using the Parikh-Wilczek tunneling method, we incorporate backreaction effects, with the emission probability being linked to the resulting change in the Bekenstein-Hawking entropy of the black hole. This probability is then used to compute the time-dependent luminosity of the system, revealing significant deviations from ideal blackbody behavior, particularly for small adS black holes. For these objects, the luminosity does not increase with temperature due to strong mass variations during evaporation. To complement this microscopic approach, we compute the renormalized energy-momentum tensor for a quantum field propagating in the Vaidya-adS geometry modelling the evaporation process. Together, these approaches clarify the interplay between geometry, quantum fields, and thermodynamics in shaping the Hawking atmosphere and the evaporation dynamics of black holes in asymptotically adS spacetimes.

In this work, we consider an interacting and matrix-valued scalar quantum field theory that emerges from a near-BPS decoupling limit of $\mathcal{N}=4$ super Yang-Mills. The theory is non-Lorentzian with SU(1,1) spacetime symmetry and admits a (semi-)local action formulation. The interaction can be viewed as arising from a non-abelian gauge field without propagating degrees of freedom. The proposed field theory action has previously been considered as classically equivalent to SU(1,1) Spin Matrix theory. In this work, we examine this equivalence at the quantum level. We show that the classical action is off-shell invariant under the SU(1,1) symmetry group. We then analyze the renormalization properties, showing the theory is finite at all orders in perturbation theory. This provides a rare example of a non-supersymmetric and non-Lorentzian quantum field theory where a non-renormalization theorem holds.

Numerical approximations to Ricci-flat Calabi–Yau metrics make it possible to move beyond the topological and holomorphic data that have traditionally dominated explicit string compactifications. This article explains what new physics and mathematics become accessible once the metric, and eventually the associated Hermitian Yang–Mills bundle data, can be computed. In heterotic compactifications, such data are needed to determine matter Kähler metrics, canonically normalized Yukawa couplings, Kaluza–Klein spectra, threshold effects, soft terms, and other non-holomorphic ingredients of the four-dimensional effective action. More broadly, numerical Calabi–Yau geometry provides quantitative input for moduli stabilization, $\alpha'$-corrected backgrounds, de~Sitter model building, axion physics, swampland distance tests, and compactifications in which the internal geometry varies over spacetime. Geometric data permit a computational approach to long-standing mathematical questions involving special Lagrangian submanifolds, SYZ fibrations, mirror symmetry, calibrated geometry, metric degeneration, restrictions of Ricci-flat metrics to fibers, and the search for analytic or semi-analytic structures. We present these directions as a roadmap for future work.

We study orbifold compactifications of heterotic strings on Enriques surfaces. We classify the inequivalent shift vectors for both the E8\times E8 and Spin(32)/Z2 lattices, and analyse the light spectrum of the resulting models. We show that these models can be interpreted as compactifications of ten-dimensional non-supersymmetric heterotic strings on Enriques surfaces. For certain classes of shifts, the moduli-independent tachyons inherited from the parent theories are projected out.

We study the decoherence induced by near-extremal charged black holes on quantum systems in their exterior. Specifically, we analyze a thought experiment recently discussed in the literature, where the quantum system is a charged particle prepared in a spatial superposition. Near-extremal black holes are known to exhibit large quantum metric fluctuations of the near-horizon geometry at low temperatures. We show that, at late times, if the black hole is sufficiently close to extremality, these quantum gravity effects make the decoherence rate vanish. This phenomenon is due to a spin-induced energy gap in the quantum black hole spectrum. For energies above the gap, the decoherence rate becomes nonzero, but is still suppressed relative to semiclassical expectations, so these quantum gravity effects always enhance the coherence of the superposition.

We consider interfaces between critical spin-chains in different universality classes, described in the continuum limit by defect/interface conformal field theory (DCFT/ICFT). We find a new conformal interface between the Tricritical Ising (TIM) and the Ising CFT. We also explore the possibility of its experimental realizations in the context of Rydberg atom arrays. Our analysis emphasizes non-invertible symmetries and consistency under modular transformations, and uses defect couplings and the defect spectrum – including in the case of mixed boundary conditions – to make sharp experimental predictions. The structure of the observables hinges on a newly discovered pattern of emergent ${W}_3$ chiral symmetry for the Tricritical-Ising/Ising interface.

We construct a $d$-dimensional dissipative colored fluid by Scherk–Schwarz reduction of a neutral viscous conformal fluid in $D=d+n$ dimensions on an $n$-dimensional unimodular group manifold. The off-diagonal components of the higher-dimensional stress tensor become non-Abelian color currents, while the higher-dimensional shear tensor induces shear, bulk-like and vector-dissipative structures in the reduced theory. We derive the map for the equation of state, sound speed, color current, entropy current and first-order transport coefficients. In particular, \[ \eta=\ee^{\alpha\varphi}\cosh\xi\,\heta,\qquad \tau=\eta\,\frac{n}{(D-1)(d-1)},\qquad \kappa=\eta\sinh^2\xi . \] We also spell out the hydrodynamic-frame issue induced by dimensional reduction, discuss the status of the internal rapidity field $\xi$, and give a detailed account of how the second law descends from the parent theory, including the roles of temperature-dependent viscosity, non-unimodular groups and possible choices for $\xi$. The construction should be regarded as a toy model for non-Abelian dissipative hydrodynamics with the potential of paving the way to direct phenomenological model of, for example, quark–gluon plasma.

Thermodynamics and transport are investigated in a holographic QCD model that extends the Einstein–Maxwell–Dilaton framework by incorporating Gauss–Bonnet corrections. Model parameters are fixed using state-of-the-art lattice QCD thermodynamics. The analysis then examines the equation of state at zero and finite baryon chemical potential, the phase structure in the temperature and chemical potential plane, as well as the shear and bulk viscosity to entropy ratios, $\eta/s$ and $\zeta/s$, via the corresponding fluctuation equations. For a constant Gauss–Bonnet coupling, the model preserves a reasonable description of the equation of state and generates a temperature-dependent $\eta/s$, although the resulting profile remains monotonic near the crossover region, which does not satisfy the phenomenological expectation. When the Gauss–Bonnet coupling is allowed to depend on the dilaton, a non-monotonic $\eta/s$ and a peaked $\zeta/s$ are obtained while maintaining agreement with thermodynamic constraints. The resulting phase diagram contains a critical end point in a phenomenologically relevant region.

Vacuum entanglement is a fundamental feature of quantum field theory exhibiting rich structure that is not completely understood. Here, we provide a complete characterization of the entanglement between two bounded spacelike-separated regions in a (1+1)-dimensional free massless real scalar field. Employing Gaussian state methods, we analytically compute the logarithmic negativity and construct closed-form solutions for the localized modes carrying it, called negativity cores. These results deepen our understanding of quantum fields and suggest extensions to higher dimensions and fermionic fields.

We define a novel class of tensor networks motivated by the Python's Lunch Conjecture (PLC) in local tensor network models of the black hole interior. We start from the observation that, for extended black brane states with short-range correlations, the PLC predicts a complexity that is smaller than the upper bound for generic short-range correlated states. We argue that the PLC makes implicit assumptions about the fine structure of the relevant tensor networks modeling gravity that render them non-generic. We demonstrate this explicitly in random tensor network models of the python's lunch, where the exponential complexity is not generally controlled by the PLC exponent. We trace the difference with the PLC to a lack of "computational covariance" in random tensor networks: while the PLC is motivated by an ability to arbitrarily decompose space into low-complexity units provided certain basic rules are followed, we show that random tensor networks do not generically have this property. We propose another class of tensor networks built from what we call "twirled perfect tensors" that do satisfy the computational covariance property and have a complexity bounded by the PLC value. We still find a discrete limitation from local postselection that appears to be absent in gravity. Moreover, we show that this class of tensor networks combines desirable holographic features of perfect tensor networks and random tensor networks, for example, it obeys a lattice Ryu-Takayanagi formula for arbitrary boundary subregions. Though motivated by holography, these tensor networks provide a flexible framework with potential applications beyond quantum gravity.

We investigate novel structures which arise from the compactification of vacuumless kinks in scalar field models coupled to impurities that preserve half the BPS sectors, described by first-order equations. We also investigate the behavior of the energy density and linear stability of the solutions. We show that compact vacuumless kinks cannot be obtained in impurity-free canonical models. By considering two distinct impurities, we study the conditions needed to induce compactification. In this scenario, stable half-compact or compact solutions are shown to emerge from the systems.

We probe poly-vector deformations of Type II backgrounds using the fundamental string, D0-brane and D3-brane, and of the 11D membrane background by the fundamental M2-brane. We show that the corresponding deformations of the world-volume theories can be written in terms of flows similar to the $\mathrm{T}\bar{\mathrm{T}}$ flow (for the D3-brane flow — with a square-root term). This interpretation works equally well for abelian (TsT) and non-abelian deformations.

Open effective field theories provide a systematic framework for describing physical systems interacting with an environment whose microscopic details are unknown, unobservable, or uncalculable. A basic step in constructing any effective field theory is the identification of the relevant degrees of freedom. For open effective theories, however, this step is subtle: their dynamics is generically dissipative and non-Hamiltonian, so the standard Hamiltonian and Lagrangian algorithms are not directly applicable. To overcome this limitation, we develop an algorithm to count degrees of freedom directly from the equations of motion. Restricting to classical, linearised dynamics on homogeneous and isotropic backgrounds, our method applies to non-Lagrangian systems with unequal numbers of fields and equations, including systems with constraints and gauge redundancies. As a by-product, our algorithm identifies constraints, gauge identities, gauge redundancies, and consistency conditions on stochastic sources. The central ingredient is the introduction of a dual set of “advanced” equations, or equivalently an auxiliary Martin-Siggia-Rose functional. We show that gauge redundancies of the original fields are associated with gauge identities of the dual advanced equations, and vice versa. We illustrate our procedure in examples ranging from coupled scalar systems to electromagnetism in a medium and gravitational effective theories relevant for cosmology. Our results will prove useful in the study of stochastic dynamics, non-equilibrium statistical systems and the semi-classical limit of open quantum systems on the Schwinger-Keldysh path integral.

We show that the one-dimensional Kuramoto-Sivashinsky (KS) equation features a scaling regime characterized by the dynamical exponent $z=1$ at intermediate scales between the large-scale Kardar-Parisi-Zhang (KPZ) scaling with $z=3/2$ and the small-scale non-universal behavior. This scaling regime is intrinsic to the KS dynamics since it arises from the vanishing of the effective viscosity when evolving from its microscopic negative KS value, to its macroscopic effective positive KPZ value. This vanishing of the viscosity deeply imprints the behavior of correlations at intermediate scales, which exhibit a universal $z=1$ scaling. This behavior pertains to the inviscid-Burgers universality class, which corresponds to the zero-viscosity fixed point of the KPZ equation. We evidence and characterize this so-far-overlooked scaling regime using both functional renormalization group and direct numerical simulations.

We investigate the effects of introducing a new vector boson on existing discrepancies within the Standard Model. Our analysis highlights the potential of this particle to alleviate these tensions while serving as a portal to the dark sector. This scenario provides a promising avenue for exploring extensions beyond the Standard Model and motivates further experimental and theoretical studies.

The analytic properties of the Jost functions are fundamental in quantum scattering theory and in the analytic continuation of the scattering matrix into the complex energy plane. In this work, the analyticity of the Jost functions is investigated from the perspective of parameter-dependent ordinary differential equations. Starting from the radial Schrödinger equation for a short-range central potential, a first-order differential system is derived for the coefficient functions associated with the Ricatti–Bessel and Ricatti–Neumann solutions. The multivalued dependence on the energy variable is shown to originate from the square-root relation between energy and momentum. By explicitly factorizing the momentum-dependent branching terms, the scattering problem is transformed into a differential system whose coefficients are single-valued analytic functions of the complex energy. Using the classical theory of analytic dependence of solutions of ordinary differential equations on parameters, it is shown that the transformed Jost functions are single-valued analytic functions of the energy variable for finite radial distance. The geometric interpretation of the factorization procedure is also discussed in terms of the topology of the associated Riemann surface.

We review recent results showing that, within the framework of quantum field theory in curved spacetime, the semiclassical energy-momentum tensor of the neutrino flavor vacuum fulfills the equation of state of dust and cold dark matter. By considering spherically symmetric spacetimes in the weak field approximation, the flavor vacuum is shown to contribute as a Yukawa correction to the Newtonian potential. We discuss how this modified potential provides a mechanism to account for the flat rotation curves of spiral galaxies. In this perspective, neutrino mixing is presented as a viable contributing factor to the dark matter content of the universe.

We show that spacetime symmetries on any background give rise to stealth vector fields obeying Proca-type equations supplemented by curvature terms. This observation, which is true for solutions of any theory of gravity and with arbitrary matter content, effectively promotes spacetime symmetries to "physical fields" whose characteristic property is that their backreaction on the geometry vanishes. In particular, this allows one to construct exact Proca hair charged and magnetized rotating black holes in all dimensions. In fact, such a construction is not limited to Killing vector fields and equally works for conformal Killing vectors and hidden symmetries encoded in Killing-Yano tensors.

Inspired by the idea that the cosmological constant can be considered as a dynamical quantity, we present a scenario bridging certain swampland conjectures from a new look at thermodynamics of black holes. Dealing with the radial metric function at the horizon as an equation of state, we discuss structural transitions and coexistence curves. By considering an effective potential with a quasi-static scalar field that could find a place in string theory, we then establish a connection between certain swampland conjectures. Relying on Kaluza Klein interpretations of scalar fields, we approach the dark dimension and dark matter through such a thermodynamic approach to charged black holes.