arXiv subjects

Tomas Reis

Publications and source records attributed to Tomas Reis.

15 recordsLinked to original sources

arXiv2026

Perturbative, Nonperturbative and Exact Aspects of Crystalline Phases in the Gross-Neveu Model

We study the crystalline phase of the $O(2N)$ Gross--Neveu model with a chemical potential for $a \leq N-2$ of the fermions. We analyze the problem in three independent ways: using perturbative QFT methods, a semiclassical large $N$ analysis, and integrability techniques (both at finite and large $N$). The resulting picture is consistent across all three approaches: at sufficiently large chemical potential $h$, an inhomogeneous phase emerges in which $a$-particle bound states condense and which, at large $N$, corresponds to a periodically oscillating chiral condensate. In this phase, the usual dynamically generated scale $\Lambda$ is replaced by two new dynamically generated scales $\Lambda_{\rm n}$ and $\Lambda_{\rm c}$. These two scales govern the multiple nonperturbative effects in the theory, corresponding in particular to the mass gaps of neutral and charged excitations on top of the inhomogeneous vacuum, respectively. They also control the nonperturbative corrections to observables such as the free energy and provide the parameters characterizing the oscillatory profile of the mean field at large $N$. In this paper, we provide the necessary details of each of the three methods, thereby complementing the results announced in a previous, shorter publication.

hep-th↗

arXiv2025

Condensates, crystals, and renormalons in the Gross-Neveu model at finite density

We study the $O(2N)$ symmetric Gross-Neveu model at finite density in the presence of a $U(1)$ chemical potential $h$ for a generic number $a \leq N-2$ of fermion fields. By combining perturbative quantum field theory, semiclassical large $N$, and Bethe ansatz techniques, we show that at finite $N$ two new dynamically generated scales $\Lambda_\mathrm{n}$ and $\Lambda_\mathrm{c}$ appear in the theory, governing the mass gap of neutral and charged fermions, respectively. Above a certain threshold value for $h$, $a$-fermion bound states condense and form an inhomogeneous configuration, which at infinite $N$ is a crystal spontaneously breaking translations. At large $h$, this crystal has mean $\Lambda_\mathrm{n}$ and spatial oscillations of amplitude $2\Lambda_\mathrm{c}$. The two scales also control the nonperturbative corrections to the free energy, resolving a puzzle concerning fractional-power renormalons and predicting new ones.

hep-th↗

arXiv2024

On the $1/c$ expansion in $2d$ CFTs with degenerate operators

We analytically determine the large central charge asymptotic expansion of the Virasoro conformal blocks entering in four-point functions with external degenerate operators on a sphere in $2d$ CFTs, and study its resurgence properties as a function of the conformal cross-ratio $z$. We focus on the cases of four heavy $(2,1)$ degenerate operators, and two $(2,1)$ heavy degenerate ones plus two arbitrary light operators. The $1/c$ asymptotic series is Borel summable for generic values of $z$, but it jumps when a Stokes line is crossed. Starting from the $1/c$ series of the identity block, we show how a resurgent analysis allows us to completely determine the other Virasoro block and in fact to reconstruct the full correlator. We also show that forbidden singularities, known to exist in correlators with two heavy and two light operators, appear with four heavy operators as well. In both cases, they are turning points emanating Stokes lines, artefacts of the asymptotic expansion, and we show how they are non perturbatively resolved. More general correlators and implications for gravitational theories in $\text{AdS}_{3}$ are briefly discussed. Our results are based on new asymptotic expansions for large parameters $(a,b,c)$ of certain hypergeometric functions $\,_2 F_1(a,b,c;z)$ which can be useful in general.

hep-th↗

arXiv2024

$\mathcal{N}=2$ SYK models with dynamical bosons and fermions

We study a class of SYK models with $\mathcal{N}=2$ supersymmetry, described by $N$ fermions in chiral Fermi multiplets, as well as $\alpha N$ first-order bosons in chiral multiplets. The interactions are characterized by two integers $(p,q)$. We focus on the large $N$ and low energy limit of these models. Despite the presence of dynamical bosons, we find conformal behavior akin to the standard SYK model. We use $\mathcal{I}$-extremization of a Witten index to study the supersymmetric solutions. In particular, we find an exact expression for the entropy, which matches the numerical solutions to the Schwinger-Dyson equations. We further solve the model both in the large $p$ and large $p,q$ limits. Numerically, we verify our analytical results and obtain estimates for the Schwarzian coupling in the near zero-temperature limit. We also study the low-lying spectrum of operators to determine the parameter ranges where the Schwarzian mode dominates the IR dynamics. Lastly, we study out-of-time-ordered correlators to show that the model is maximally chaotic.

hep-th↗

arXiv2023

An anharmonic alliance: exact WKB meets EPT

Certain quantum mechanical systems with a discrete spectrum, whose observables are given by a transseries in $\hbar$, were shown to admit $\hbar_0$-deformations with Borel resummable expansions which reproduce the original model at $\hbar_0=\hbar$. Such expansions were dubbed Exact Perturbation Theory (EPT). We investigate how the above results can be obtained within the framework of the exact WKB method by studying the spectrum of polynomial quantum mechanical systems. Within exact WKB, energy eigenvalues are determined by exact quantization conditions defined in terms of Voros symbols $a_{γ_i}$, $γ_i$ being their associated cycles, and generally give rise to transseries in $\hbar$. After reviewing how the Borel summability of energy eigenvalues in the quartic anharmonic potential emerges in exact WKB, we extend it to higher order anharmonic potentials with quantum corrections. We then show that any polynomial potential can be $\hbar_0$-deformed to a model where the exact quantization condition reads simply $a_γ=-1$ and leads to the EPT Borel resummable series for all energy eigenvalues.

hep-th↗

arXiv2023

Instantons, renormalons and the theta angle in integrable sigma models

Some sigma models which admit a theta angle are integrable at both $\vartheta=0$ and $\vartheta=π$. This includes the well-known $O(3)$ sigma model and two families of coset sigma models studied by Fendley. We consider the ground state energy of these models in the presence of a magnetic field, which can be computed with the Bethe ansatz. We obtain explicit results for its non-perturbative corrections and we study the effect of the theta angle on them. We show that imaginary, exponentially small corrections due to renormalons remain unchanged, while instanton corrections change sign, as expected. We find in addition corrections due to renormalons which also change sign as we turn on the theta angle. Based on these results we present an explicit non-perturbative formula for the topological susceptibility of the $O(3)$ sigma model in the presence of a magnetic field, in the weak coupling limit.

hep-th↗

arXiv2023

On the resurgence of renormalons in integrable theories

In this thesis we explore the physics of renormalons in integrable models under the framework of resurgence. In the first part, we review some background on resurgence, integrability and renormalons, including a discussion of large N renormalons and ring diagrams. In the second part, we start from the Bethe ansatz integral equations and obtain exact trans-series for the free energy in multiple models. These trans-series include non-perturbative effects which correspond to renormalons at unexpected positions in the Borel plane. We test the trans-series numerically and at large N. We also study what happens to these trans-series under a topological angle. In the third part, we use apply the techniques of resurgence in non-relativistic theories. We find a relation between the energy gap of the system and the positions of singularities in the Borel plane. By studying the asymptotic behaviour of ring diagrams, we identify this relation with renormalons.

hep-th↗

arXiv2023

New renormalons from analytic trans-series

We study the free energy of integrable, asymptotically free field theories in two dimensions coupled to a conserved charge. We develop methods to obtain analytic expressions for its trans-series expansion, directly from the Bethe ansatz equations, and we use this result to determine the structure of its Borel singularities. We find a new class of infrared renormalons which does not fit the traditional expectations of renormalon physics proposed long ago by 't Hooft and Parisi. We check the existence of these new singularities with detailed calculations based on the resurgent analysis of the perturbative expansion. Our results show that the structure of renormalons in asymptotically free theories is more subtle than previously thought, and that large $N$ estimates of their location might be misleading.

hep-th↗

arXiv2021

Resurgence and renormalons in the one-dimensional Hubbard model

We use resurgent analysis to study non-perturbative aspects of the one-dimensional, multicomponent Hubbard model with an attractive interaction and arbitrary filling. In the two-component case, we show that the leading Borel singularity of the perturbative series for the ground-state energy is determined by the energy gap, as expected for superconducting systems. This singularity turns out to be of the renormalon type, and we identify a class of diagrams leading to the correct factorial growth. As a consequence of our analysis, we propose an explicit expression for the energy gap at weak coupling in the multi-component Hubbard model, at next-to-leading order in the coupling constant. In the two-component, half-filled case, we use the Bethe ansatz solution to determine the full trans-series for the ground state energy, and the exact form of its Stokes discontinuity.

hep-th↗

arXiv2021

Testing the Bethe ansatz with large N renormalons

The ground state energy of integrable asymptotically free theories can be conjecturally computed by using the Bethe ansatz, once the theory has been coupled to an external potential through a conserved charge. This leads to a precise prediction for the perturbative expansion of the energy. We provide a non-trivial test of this prediction in the non-linear sigma model and its supersymmetric extension, by calculating analytically the associated Feynman diagrams at next-to-leading order in the $1/N$ expansion, and at all loops. By investigating the large order behaviour of the diagrams, we locate the position of the renormalons of the theory and we obtain an analytic expression for the large $N$ trans-series associated to each. As a spin-off of our calculation, we provide a direct derivation of the beta function of these theories, at next-to-leading order in the $1/N$ expansion.

hep-th↗

arXiv2021

Renormalons in integrable field theories

In integrable field theories in two dimensions, the Bethe ansatz can be used to compute exactly the ground state energy in the presence of an external field coupled to a conserved charge. We generalize previous results by Volin and we extract analytic results for the perturbative expansion of this observable, up to very high order, in various asymptotically free theories: the non-linear sigma model and its supersymmetric extension, the Gross--Neveu model, and the principal chiral field. We study the large order behavior of these perturbative series and we give strong evidence that, as expected, it is controlled by renormalons. Our analysis is sensitive to the next-to-leading correction to the asymptotics, which involves the first two coefficients of the beta function.

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arXiv2020

Three roads to the energy gap

We determine analytically the energy gap at weak coupling in the attractive multi-component Gaudin--Yang model, an integrable model which describes interacting fermions in one dimension with $κ$ components. We use three different methods. The first one is based on a direct analysis of the Bethe ansatz equations. The second method uses the theory of resurgence and the large order behavior of the perturbative series for the ground state energy. The third method is based on a renormalization group analysis. The three methods lead to the same answer, providing in this way a non-trivial test of the ideas of resurgence and renormalons as applied to non-relativistic many-body systems.

hep-th↗

arXiv2020

A new renormalon in two dimensions

According to standard lore, perturbative series of super-renormalizable theories have only instanton singularities. In this paper we show that two-dimensional scalar theories with a spontaneously broken $O(N)$ symmetry at the classical level, which are super-renormalizable, have an IR renormalon singularity at large $N$. Since perturbative expansions in these theories are made around the "false vacuum" in which the global symmetry is broken, this singularity can be regarded as a manifestation of the non-perturbative absence of Goldstone bosons. We conjecture that the Borel singularity in the ground state energy of the Lieb--Liniger model is a non-relativistic manifestation of this phenomenon. We also provide {\it en passant} a detailed perturbative calculation of the Lieb--Liniger energy up to two-loops, and we check that it agrees with the prediction of the Bethe ansatz.

hep-th↗

arXiv2019

Resurgence for superconductors

An important non-perturbative effect in quantum physics is the energy gap of superconductors, which is exponentially small in the coupling constant. A natural question is whether this effect can be incorporated in the theory of resurgence. In this paper we take some steps in this direction. We conjecture that the perturbative series for the ground state energy of a superconductor is factorially divergent, and that its leading Borel singularity is governed by the superconducting energy gap. We test this conjecture in detail in the attractive Gaudin-Yang model, an exactly solvable model in one dimension with a BCS-like ground state. In order to do this, we develop techniques to calculate the exact perturbative series of its ground state energy up to high order. We also argue that the Borel singularity is of the renormalon type, and we identify a class of diagrams leading to factorial growth. We give additional evidence for the conjecture in other models.

hep-th↗

arXiv2019

Exact perturbative results for the Lieb-Liniger and Gaudin-Yang models

We present a systematic procedure to extract the perturbative series for the ground state energy density in the Lieb-Liniger and Gaudin-Yang models, starting from the Bethe ansatz solution. This makes it possible to calculate explicitly the coefficients of these series and to study their large order behavior. We find that both series diverge factorially and are not Borel summable. In the case of the Gaudin-Yang model, the first Borel singularity is determined by the non-perturbative energy gap. This provides a new perspective on the Cooper instability.

math-ph↗