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Related papers: Modular resurgent structures

200 papers

Many observables in quantum field theory can be expressed in terms of trans-series, in which one adds to the perturbative series a typically infinite sum of exponentially small corrections, due to instantons or to renormalons. Even after…

High Energy Physics - Theory · Physics 2025-08-04 Marcos Marino , Ramon Miravitllas , Tomás Reis

In the previous papers, the authors pointed out correspondence between a supersymmetric double-well matrix model and two-dimensional type IIA superstring theory on a Ramond-Ramond background. This was confirmed by agreement between planar…

High Energy Physics - Theory · Physics 2019-06-26 Tsunehide Kuroki , Fumihiko Sugino

This paper is a continuation of our previous work \cite{St} where we have studied the Stokes phenomenon for a particular family of equation \eqref{initial} with \eqref{form-0}-\eqref{npe} from a perturbative point of view. Here we focus on…

Classical Analysis and ODEs · Mathematics 2019-06-25 Tsvetana Stoyanova

We analyze truncated series generated as divergent formal solutions of non-linear ordinary differential equations. Motivating the study is a specific non-linear, first-order differential equation, which is the basis of the resurgent…

Mathematical Physics · Physics 2024-10-03 Alessio Maiezza , Juan Carlos Vasquez

A set of four introductory lectures on Resurgent Asymptotics for Physics (``resurgence") at the CERN Summer School: Continuum Foundations of Lattice Gauge Theories, July 2024. Lecture 1: The Airy function and the Stokes phenomenon. Lecture…

High Energy Physics - Theory · Physics 2026-04-27 Gerald V. Dunne

We perform an all-order resurgence analysis of a quantum field theory renormalon that contributes to an anomalous dimension in six-dimensional scalar $\phi^3$ theory and is governed by a third-order nonlinear differential equation. We…

High Energy Physics - Theory · Physics 2022-06-16 Michael Borinsky , David Broadhurst

We analyze the Moyal star product in deformation quantization from the resurgence theory perspective. By putting algebraic conditions on Borel transforms, one can define the space of ``algebro-resurgent series'' (a subspace of $1$-Gevrey…

Mathematical Physics · Physics 2021-01-01 Yong Li , David Sauzin , Shanzhong Sun

In 2010, Zagier described a new phenomenon which he called quantum modularity. This connected various examples coming from disparate fields which exhibit near-modular behavior. In the fifteen years since, Zagier's philosophy has informed…

Number Theory · Mathematics 2025-06-02 Eleanor McSpirit , Larry Rolen

For analytic nonlinear systems of ordinary differential equations, under some non-degeneracy and integrability conditions we prove that the formal exponential series solutions (trans-series) at an irregular singularity of rank one are Borel…

Classical Analysis and ODEs · Mathematics 2007-05-23 O. Costin

The resurgence and asymptotic resurgence of an ideal in a polynomial ring are two statistics which measure the relationship between its regular and symbolic powers. We address two aspects of resurgence which can be studied via asymptotic…

Commutative Algebra · Mathematics 2020-07-30 Michael DiPasquale , Ben Drabkin

We provide estimates for the convolution product of an arbitrary number of "resurgent functions", that is holomorphic germs at the origin of $C$ that admit analytic continuation outside a closed discrete subset of $C$ which is stable under…

Dynamical Systems · Mathematics 2014-04-22 David Sauzin

We study non-perturbative effects of torus partition function of the $T\bar{T}$-deformed 2d CFTs by resurgence. The deformed partition function can be written as an infinite series of the deformation parameter $\lambda$. We develop highly…

High Energy Physics - Theory · Physics 2024-10-28 Jie Gu , Yunfeng Jiang , Huajia Wang

This paper investigates some issues arising in categorical models of reversible logic and computation. Our claim is that the structural (coherence) isomorphisms of these categorical models, although generally overlooked, have decidedly…

Category Theory · Mathematics 2013-04-29 Peter Hines

We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…

Logic · Mathematics 2021-12-21 Matthias Kunik

We discuss some physical consequences of the resurgent structure of Painleve equations and their related conformal block expansions. The resurgent structure of Painleve equations is particularly transparent when expressed in terms of…

High Energy Physics - Theory · Physics 2019-10-25 Gerald V. Dunne

In this work, we analyze perturbative expansions of the quantum metric tensor (QMT) in anharmonic oscillators, focusing on quartic, sextic, and $d$-dimensional models. Using high-order perturbation theory, we show that the divergent QMT…

Quantum Physics · Physics 2025-10-31 Marcos J. Hernández , Bogar Díaz , J. David Vergara

Stokes phenomenon refers to the fact that the asymptotic expansion of complex functions can differ in different regions of the complex plane, and that beyond the so-called Stokes lines has an unphysical divergence. An important special case…

Quantum Physics · Physics 2018-04-04 Werner Koch , David J. Tannor

Using a method mixing Mellin-Barnes representation and Borel resummation we show how to obtain hyperasymptotic expansions from the (divergent) formal power series which follow from the perturbative evaluation of arbitrary "$N$-point"…

High Energy Physics - Theory · Physics 2014-11-20 Samuel Friot , David Greynat

We study the perturbative expansion of the ground state energy in the presence of an external field coupled to a conserved charge in the integrable two-dimensional O$(4)$ nonlinear sigma model. By solving Volin's algebraic equations for the…

High Energy Physics - Theory · Physics 2022-04-27 Zoltán Bajnok , János Balog , István Vona

We consider certain Lambert series as generating functions of divisor sums twisted by Dirichlet characters and compute their exact resurgent transseries expansion near $q=1^-$. For special values of the parameters, these Lambert series are…

Number Theory · Mathematics 2025-07-30 David Broadhurst , Daniele Dorigoni