Papers

We investigate the thermodynamics, criticality, and selected radiative and optical properties of an Euler-Heisenberg AdS black hole surrounded by quintessence, perfect fluid dark matter, and a cloud of strings. Within the extended phase-space formalism, we derive the thermodynamic quantities, verify the modified first law and Smarr relation, and analyze the corresponding equation of state and critical behavior. We show that the Euler–Heisenberg coupling and the surrounding matter fields substantially modify the temperature profile, the stability structure, and the location of the critical point. We also examine the sparsity of Hawking radiation, together with the photon sphere, black hole shadow, and the associated geometric-optics emission rate.

One of the most important applications of topological recursion concerns spectral curves for which the functions $(x,y)$ defining the spectral curve are allowed to have logarithmic singularities. This occurs for instance for Seiberg-Witten curves and mirror curves computing Gromov–Witten invariants of toric Calabi–Yau threefolds. A recently introduced extension of topological recursion, the so-called logarithmic topological recursion, exhibits the correct behavior under certain limits of those spectral curves. In this article, we derive the dilaton equations in the setting of logarithmic topological recursion, as well as variational formulas, and provide a definition of the free energies in situations where standard topological recursion was known to fail. We present examples in which the new definition of the free energies directly (without any computation) reproduces the full perturbative part of the Nekrasov–Shatashvili partition function of 4d $\mathcal{N}=2$ pure supersymmetric gauge theory, as well as the all-genus free energies of mirror curves of strip geometries, including in particular the topological vertex and the resolved conifold.

We investigate a pre-inflationary dynamical compactification scenario in which a higher-dimensional expanding universe evolves into an effectively four-dimensional one through curvature-assisted modulus trapping. To obtain a calculable semiclassical realization, we consider a simple five-dimensional $S^1$ compactification in a time-dependent open FRW background. Bulk quantum fields generate both the late-time Casimir contribution that stabilizes the radion and the early-time Kaluza-Klein thermal contributions relevant for the cosmological evolution. We show that negative curvature can sustain tracker-like radion evolution, allowing the radion to be trapped in a compactified vacuum before a subsequent four-dimensional inflationary phase dilutes the curvature remnant. While our analysis is performed in a 5D toy model, it illustrates a broader mechanism by which dynamical compactification can arise in a pre-inflationary higher-dimensional cosmology.

The type IIB matrix model has been proposed as a nonperturbative formulation of superstring theory. While numerical simulations of this model are essential for probing nonperturbative effects, such as the emergence of time and an expanding 3–dimensional space, they are hindered by the sign problem. We address this using the Complex Langevin Method (CLM). Furthermore, to suppress spurious numerical artifacts that originate from large Lorentz boosts due to the Lorentz symmetry of the model, we nonperturbatively fix the Lorentz symmetry using the Faddeev–Popov procedure. We then study this model to investigate the impact of supersymmetry on the dynamical generation of (3+1)–dimensional spacetime.

We study the trajectories of massive particles in spherically symmetric black holes in arbitrary dimensions, and find certain universal features based on the topological classification of the fixed points. If the system admits a center, we find two possible outcomes: regardless of the value of the angular momentum, the center always survives, which is realized in global AdS spacetimes or, the center disappears below a critical value of angular momentum, which happens for various spherically symmetric black holes. For the latter case, we find that irrespective of the details of the black hole, there must always be a saddle point. Topological arguments show that there exists a certain critical value of energy, angular momentum and the angular velocity, where the center and the saddle coalesce. This happens at a special point in the parameter space where the trajectories are the limiting innermost stable circular orbits (ISCOs). At the critical point, conserved quantities show universal, van der Waals-like mean-field scaling typical of a second-order phase transition. The anomalous dimensions $\gamma$ of the double-twist operators in the CFT are found, both using AdS/CFT and through the the heavy-heavy-light-light four point correlators, giving negative and positive values for the center and saddle, respectively, including the emergence of certain non-analytic behaviour at the ISCO. For the center, we also find subleading corrections in $\frac{1}{\Delta_H}$ to $\gamma$ in the dual CFT, and dsicuss the implications of our results.

Many extensions of the Standard Model (SM) generically introduce new sources of CP violation, which can induce observable $P$-odd and $T$-odd permanent electric dipole moments (EDMs) of nuclei, atoms, and molecules. A future observation of nonvanishing EDMs would therefore provide a sensitive probe of physics beyond the SM, while also posing a nontrivial inverse problem: identifying their underlying ultraviolet origin. In this work, we identify six representative classes of CP-violating effective operators near the QCD scale, including the QCD $\theta$-term, that are particularly relevant for low-energy EDMs and can arise in a broad range of SM extensions. We show that these operator classes lead to distinct EDM patterns across different systems, thereby enabling discrimination among them through experimentally measured EDMs. We further emphasize that EDM measurements can shed light on the origin of the vacuum expectation value of the QCD axion. In particular, they may help distinguish whether a nonzero axion vacuum expectation value is predominantly induced by high-scale Peccei–Quinn symmetry-breaking effects, such as those associated with quantum gravity, or by the interplay between beyond-the-SM CP violation and the QCD anomaly.

We probe the thermodynamic phase structure of four dimensional Horava Lifshitz black holes by Lyapunov exponent analysis. For both massless and massive test particles, the Lyapunov exponent exhibits a multivalued dependence on temperature in regimes with a first-order phase transition, with distinct branches corresponding to small, intermediate, and large black hole phases, and this behaviour disappears at the critical point. The discontinuity in the Lyapunov exponent acts as an effective order parameter with critical exponent $\delta=1/2$, consistent with mean-field universality. We also find that the chaos bound is generically violated below a threshold horizon radius, with the violation occurring within the thermodynamically stable phase and persisting even in the absence of a phase transition. These results establish the robustness and universality of Lyapunov exponents as probes of black hole thermodynamics in alternative theories of gravity.

This is part I of a series of papers in which we investigate the role of spectral networks in quantum Liouville theory, with particular emphasis on spectral networks of Fenchel-Nielsen type. In this part, we focus on the computation of $SL(2, \mathbb C)$ quantum parallel transports on any (punctured) Riemann surface $C$, which in quantum Liouville theory has a well-known prescription through the Moore-Seiberg formalism. Our main achievement is rederiving this prescription through an extension of the $q$-nonabelianisation formalism applied to spectral networks of Fenchel-Nielsen type. One of the spin-offs is a proposal for a quantum version of the NRS proposal.

In this paper, we elaborate on the connection between leading singularities and canonical bases of Feynman integrals beyond polylogarithms. We start by discussing a notion of leading singularities in dimensional regularization, which can be generalized from the Riemann sphere to more complex geometries, and use it to demonstrate how selecting Feynman integrals with unit leading singularities necessitates introducing new transcendental functions related to the periods of the underlying geometries. Integrals with unit leading singularities in this generalized sense, satisfy $\epsilon$-factorized differential equations, and the new transcendental functions are in direct correspondence to the new differential forms appearing in their Gauss-Manin connection. We argue that this construction is mathematically equivalent to the splitting of the period matrix into semi-simple and unipotent parts plus a clean-up step, and demonstrate its use with examples of increasing complexity that require the interplay of multiple geometries.

We investigate the dynamics of massive test particles around a static black hole in nonlocal gravity and examine the corresponding properties of HF QPOs, constraining the nonlocal parameter to $\alpha/M \leq 0.452$. The nonlocal parameter $\alpha$ enhances the effective potential $V_{eff}$ and leads to a systematic reduction in the energy E and angular momentum L of circular orbits. Consequently, the ISCO radius, along with the associated energy and angular momentum, decreases monotonically with $\alpha$, while the radiative efficiency increases, reaching a maximum of approximately $8.9\%$. Due to the spherical symmetry of the spacetime, the Keplerian frequency $\Omega_{\phi}$ and the vertical epicyclic frequency $\Omega_{\theta}$ coincide and are suppressed by $\alpha$, whereas the radial epicyclic frequency $\Omega_{r}$ is enhanced. The impact of $\alpha$ on several twin-peak HF QPO models is examined, revealing that $\alpha$ increases both the lower and upper bounds of the predicted QPO frequency ranges. By imposing the $2\nu_U = 3\nu_L$ resonance condition, we analyze the resonant radius, upper QPO frequency, maximum allowed black hole mass, and the time delay between the shadow and QPO signals. We find that the resonant radius decreases with $\alpha$, while the upper QPO frequency increases, spanning the range $\nu_U \sim(673/M-4360/M)$Hz. When the TOV imit is imposed, the upper frequency is further constrained to $\nu_U \lesssim 1450$Hz. Combining astronomical observations for the classification of QPOs, where $\nu_U \geq 100$Hz, the black hole mass in the nonlocal gravity should satisfy $M \lesssim 43.6M_\odot$. Although the radial separation between the resonant radius and the photon sphere decreases with $\alpha$, the associated gravitational time delay increases, remaining below $\sim 1.3$ms and thus negligible for current observational capabilities.

We investigate the Wheeler-DeWitt equation for a flat, homogeneous, and isotropic Universe containing a canonical scalar field with a potential. We show that under the constraint $|\Psi|=1$, where the Wheeler-DeWitt equation exactly becomes the classical Hamilton-Jacobi equation, the form of the potential is completely determined depending on the value of the operator ordering parameter. Furthermore, we demonstrate that the classified potentials admit simple forms, such as the exponential, quadratic with a negative cosmological constant, and cosine-type potential with a negative cosmological constant. Several of these have already been explored in the context of inflation or dark energy. Finally, focusing on the system with the cosine-type potential and a negative cosmological constant in the classified potentials, we derive the analytical solutions for the scale factor and the scalar field and discuss the cosmological implications.

We analyze the nonabelian surface holonomy on a bipartite hypercubic lattice following a proposal in arXiv:1002.4636 [hep-th]. The bipartite structure of the lattice enables us to introduce spike string configurations. These spikes play a crucial role for the time evolution of the string when the total number of color indices changes.

Early-time evolution away from an unstable equilibrium in a nonlinear system is often expected to be governed by the associated linear instability. Combining full nonlinear evolution with first- and second-order quasinormal mode (QNM) calculations, we show that this expectation can fail during the unstable growth stage of a Q-ball hairy black hole in Einstein-Maxwell theory with a charged self-interacting scalar field. The linear unstable QNM has a much larger amplitude in one component of the scalar field than in the other: the more strongly responding component follows that mode, whereas the early growth of the more weakly responding component is dominated by a second-order QNM sourced by the linear unstable mode. This occurs while the evolution remains perturbative. Our results thus show that the early growth of an individual component need not be governed by its linear response.

While the positive Grassmannian is deeply understood through the rich combinatorics of plabic graphs and positroid cells, its tropical counterpart, the positive tropical Grassmannian Trop$_{>0}G(k,n)$, has lacked a comparable structural framework for general $k$. Both the global face structure of Trop$_{>0}G(k,n)$ and the internal metric geometry of the tropical linear spaces it parametrizes have remained largely uncharted. This paper develops a systematic algebraic and polyhedral foundation that resolves this gap. The engine of our framework is a fundamental tropical duality, analogous to the duality between cluster variables (or more precisely, their $u$-coordinates) and $\mathbf{g}$-vectors, pairing two families of objects introduced by the first author: the planar basis of tropical Plücker vectors and the planar cross-ratios on the positive configuration space. We prove that this duality links the fan structure of the positive tropical Grassmannian to the noncrossing fan of Santos, Stump, and Welker, yielding a global bijection between integer points of $Trop_{>0}G(k,n)$ and noncrossing tableaux. We then study how this discrete combinatorial data controls the continuous metric geometry of positive tropical linear spaces. We realize the bounded complex of an integer positive tropical linear space as the subdifferential of a central roof function on the hypersimplex, and use this realization to embed it into a dilate of the fundamental alcoved simplex. The dilation factor, and hence the geometric diameter of the complex, is governed by a single invariant, the planar kinematics ($K) weight, which we show equals the number of columns in the associated noncrossing tableau. The results of this work are applied in our parallel work on scaffolds for higher tropical Grassmannians.

Scaffolds are the one-dimensional skeleta of high-dimensional flag simplicial complexes of nonpositive curvature. They generalize the phylogenetic trees of Trop G(2,n) to arbitrary $k$, drawing together SL(k)-web bases, affine buildings, the combinatorics of the positive tropical Grassmannian and low-dimensional topology. We prove that scaffolds model points in all tropical Grassmannians via a $k$-point distance function. In this paper, we study in detail CAT(0) planar graphs, which are positive scaffolds for the tropical Grassmannian of three-planes. CAT(0) planar graphs are directed versions of the diskoids of Fontaine-Kamnitzer-Kuperberg, planar dual to SL(3)-webs. Our main result is the construction of a unique representation of any given integer positive tropical Plucker vector by a normal CAT(0) planar graph. We show that any normal CAT(0) planar graph embeds into the tropical linear space as a Lam-Postnikov membrane, and embeds into the Keel-Tevelev membrane within the affine building. We show that Early's planar basis expansion can be computed directly from the strand combinatorics of the dual web, and connect this expansion to Petersen-Pylyavskyy-Speyer's noncrossing tableaux, explored further in our companion paper.

We present a minimal basis for non-derivative baryon-number-violating operators in the Standard Model Effective Field Theory up to mass dimension 11, as well as for the $(\Delta B,\Delta L) = (2,2)$ and $(2,-2)$ operators at dimension 12. Compared to existing results, our bases generally contain fewer terms and simpler contractions, although we also highlight select cases where a minimal basis is incompatible with simple structures.

We present a covariant quantization of the first-order formulation of the Einstein-Hilbert theory using the path integral and BV formalisms. In this approach, the metric $g^{\mu\nu}$ and the connection $\Gamma^\lambda_{\mu\nu}$ are treated as independent, with the connection playing the role of an auxiliary field. We show that the gauge algebra is closed and irreducible. We further demonstrate that the Dyson-Schwinger equations in the first-order formulation lead to structural identities that constrain the Green's functions of the auxiliary field and encode the classical equations of motion at the quantum level. We revisit the quantum equivalence between the first- and second-order formulations of the Einstein-Hilbert theory. By employing a suitable trick, a manifestly covariant form of the Senjanović measure is derived. We also show that the two formulations are equivalent at the level of the effective action when the auxiliary field is on-shell.

We show that it is possible to use dimensional regularization (DR) beyond the usual $\varepsilon$-expansion in the context of renormalization group (RG) calculations in Critical Phenomena. Based on this fact, we propose a new functional RG scheme - Functional Dimensional Regularization (FDR) - and apply it to a scalar theory in three dimensions. We compute the critical exponents of the Ising universality class directly in $d=3$ under various typical approximations. The method that emerges combines the agility typical of DR with the generality proper of functional RG. Moreover, at a given order of approximation, FDR seems to provide faster convergence and better estimates than other functional RGs.

Although asymptotically flat black holes generically lack thermodynamic phase transitions, we show that curvature-induced scalarization of electrically charged black holes in Einstein-Maxwell-scalar-Gauss-Bonnet theory provides a natural setting for nontrivial thermodynamic behavior, without invoking external confining mechanisms or an extended thermodynamic formalism. Working within the canonical ensemble and employing the Euclidean approach, we identify the coexistence of locally stable scalarized and Reissner-Nordström thermal states, which promotes free-energy crossings to bona fide phase transitions between equilibrium phases. For weak coupling, a second-order phase transition coincides with the second bifurcation point, at which the scalarized branch reconnects with the Reissner-Nordström branch and scalar hair is spontaneously shed. As the coupling strength increases, this transition becomes zeroth order, the scalarized branch shrinks, and a fish-like structure develops in its Helmholtz free energy, rendering locally stable thermal states partially metastable, and yielding up to three phase transitions. In the strong-coupling limit, the scalarized branch reduces to a Schwarzschild-like solution, and the Reissner-Nordström phase ultimately emerges as the sole thermodynamically preferred configuration.

The IKKT matrix model, which is proposed as a non-perturbative formulation of superstring theory, has an issue typical of zero-dimensional theory – ambiguity in the definition of its path integral. To tackle this issue, we revisit the path-integral formulation of perturbative string theory. In this article, we review recent progress in the string world-sheet path-integral formulation, especially in the Minkowski signature. We first derive the Minkowskian path integral of the Nambu-Goto type equivalent to Polyakov's Euclidean path integral for critical closed string theory, showing equivalences among the Nambu-Goto-, Schild- and Polyakov-type formulations both in the Minkowskian and Euclidean signatures. We also show that “stringy causality” is realised in the path-integral formulation at the level of string perturbation theory. We then obtain the matrix model with a property like the stringy causality, which turns out to be a Minkowskian version of the NBI-type IKKT matrix model, by matrix regularisation of the path integral for perturbative type IIB string theory.

We analyse the laws of thermodynamics governing the behaviour of cosmological horizons in de Sitter space and their map to a holographic description at future infinity, $\mathcal{I}^+$. In this case, the boundary can receive signals from two cosmological horizons. We find a universal form for the first law of thermodynamics, valid in general circumstances, when matter-energy crosses both horizons and impinges on the boundary. This universal form leads to a well defined notion of entropy in the holographic dual. It is specified on a co-dimension one surface of the boundary, and can be expressed as a function of two boundary charges, pressure and angular momentum, both of which are derived from the Brown-York stress tensor. Additional comments on the second law, confusing factors of $i$ which arise, and comments pertaining to JT gravity, are included towards the end.

Quantum entanglement between gamma-ray photons emitted following electron-positron annihilation is expected to be maximal and may be characterized via non-classical polarization correlations. However, this is difficult to verify experimentally because there are no established schemes that approach ideal projective-polarization measurements for high-energy photons. Hence, polarization entanglement between MeV-scale annihilation photons has not yet been conclusively demonstrated. We develop here a framework that models polarization measurements of high-energy photons via Compton polarimetry, employing the formalism of positive operator-valued measures (POVMs). We extend the POVM description to sequences of repeated interactions and show that the measurement converges toward an ideal projective measurement of linear polarization as the number of interactions increases. We demonstrate that this progressive improvement in measurement sharpness can enable the experimental violation of CHSH inequalities.

Neural architectures trained with losses inspired by differential conditions are the basis for PINN models. Since many constructions in differential geometry may be framed as minimisation of a differential functional, these functionals can be coded as loss functions to align the AI loss-minimisation goal with that of solving the geometric problem. This contribution to the Recent Progress in Computational String Geometry workshop proceedings introduces the PINN architecture defining principles, motivates how they are well suited for problems in differential geometry, and demonstrates their use via summaries of three works at this intersection.

We propose and analyze a new method of detecting center vortices and monopoles in lattice Yang-Mills theory. This procedure is sensitive to the intrinsic degeneracy of the center charges, which play a crucial role in how these topological objects interact and correlate with one another. Our approach is based on fixing the Maximal Abelian gauge (MAG) and decomposing the link configuration in a suitable way to look for so-called Cartan fluxes, by projecting the gauge fields onto the Cartan subalgebra. The method directly assigns the detection of monopoles to the roots of the gauge group, allowing a clearer and more robust characterization of the Abelian-charge content of the gauge configuration. Our discussion is general for $SU(N)$ gauge theory, but we focus our applications on the $SU(3)$ case. For the $SU(2)$ case, our proposed parametrization is equivalent to the standard one. We present a numerical study of the monopole density in $SU(3)$ theory, obtained using our method. A sizable difference in the number of monopoles is found between our proposed method and the standard one. Also, we observe a Weyl-symmetric distribution of monopole charges.

We study the analytic properties and three equivalent representations of the Toller matrices $T^{(\pm)}$ which appear in the causal formulation of spinfoam transition amplitudes for 4d Lorentzian quantum gravity. These are polynomially bounded functions on the Lorentz group which satisfy the relation $T^{(+)}+T^{(-)}=D$, where the Wigner matrix $D$ provides a unitary irreducible representation of $SL(2,C)$. Ruhl's definition of $T^{(\pm)}$ in terms of analyticity and asymptotic properties is shown to be equivalent to the recently introduced Feynman $i\varepsilon$ prescription in spinfoams. We show that, equivalently, they can be represented as an integral over eigenvalues of the boost operator, which results in a sum over residues. The latter reproduces the Wick rotation relating Euclidean $Spin(4)$ to Lorentzian $SL(2,C)$ spinfoams studied by Dona, Gozzini and Nicotra. We provide explicit expressions in terms of hypergeometric functions and specialize them to the $\gamma$-simple representations relevant for spinfoams.

The two-dimensional hyperbolic plane, $\mathbb{H}^2$, is an unusual system in that dimensionality changes with scale: locally two-dimensional and planar at short distances, but effectively infinite-dimensional at large scales, it provides an interesting paradigm for the study of (quantum) phase transitions, notably the disorder-driven Anderson transition. Generalizing previous work, which treated short and large distance scales separately, we develop a unified framework interpolating between the principles of low- and high-dimensional Anderson localization. As a main result, we derive a two-parameter flow in a plane spanned by scale-dependent curvature (setting the system's effective dimensionality) and conductivity, with an extended critical line separating metallic and insulating phases.

Self-dual theories are powerful toy models of their completions. It was shown recently that there are infinitely many SD-theories once massless higher-spin fields are allowed. The maximal SD-theory is chiral higher-spin gravity. Following the recent [arxiv:2602.12176] we show that all SD-theories, including those with massless higher-spin fields, have nontrivial tree-level amplitudes in Kleinian signature or complex Minkowski kinematics. Within celestial holography, the nontriviality of amplitudes in chiral higher-spin gravity provides the missing ingredient needed to complete the celestial analogue of the vector-model/higher-spin AdS/CFT duality.

The $(1+1)$-dimensional chiral anomaly is a paradigmatic exact result in quantum field theory, traditionally formulated for zero-temperature pure states where it arises from spectral flow induced by external gauge fields and captures universal ground-state properties. In mixed states, however, the participation of many states and charge exchange with the environment invalidate this mechanism. Naive extensions yield model-dependent anomaly coefficients, calling its universality into question. Here, we resolve this problem for Abelian symmetries by deriving the anomaly from an algebraic relation between the symmetry and its flux-insertion operator. We obtain symmetry-charge flow, a mixed-state generalization of spectral flow, in which an applied field redistributes statistical weight across symmetry-resolved charge sectors. Fixed solely by symmetry, the anomaly restores universality and applies to both pure and mixed states in fermionic and bosonic systems. We substantiate these results in tight-binding fermionic models with continuous symmetry and in spin models with discrete symmetries.

This article discusses incorrect statements appearing in textbooks on quantum field theory (QFT); some of these mistakes also appear in the research literature. The focus is not on errors made by an individual author, but on conceptual muddledness that is widespread in introductory textbooks. We start from a bare-bones summary of QFT, meant to establish the notation. We then turn to our six paradigmatic themes, in each case quoting a specific example of the textbook mistake, a summary of material that is known to experts but is frequently mishandled in introductory works, pointers to authoritative references where the relevant concept is handled properly, as well as a concise correction that rectifies any issues. The goal of this work is to warn readers of the existence of several pitfalls and thereby stop these errors from further propagating in the literature on QFT.

We propose a general framework for integrable field theories in arbitrary spacetime dimension $d+1$ which is based on $d$-term $L_\infty$-algebras. Specifically, we introduce cyclic $L_\infty$-algebras describing topological-holomorphic higher Chern-Simons theories on $M \times \mathbb{C}P^1$ with suitable singularity structures and boundary conditions, controlled by a meromorphic $1$-form on $\mathbb{C}P^1$. Using homological perturbation theory and homotopy transfer, we construct weakly equivalent models describing $(d+1)$-dimensional field theories on $M$. Their integrability is witnessed by a natural map to an $L_\infty$-algebra describing higher Lax connections, yielding conserved charges associated with higher-dimensional cycles in $M$. The resulting theories admit natural action functionals and recover the Costello-Yamazaki construction in $2$ dimensions.