Resurgence in the O(4) sigma model

TL;DR

This paper investigates the resurgence structure of the free energy in the integrable two-dimensional O(4) sigma model under a magnetic field, using high-precision perturbative data and asymptotic analysis.

Contribution

It introduces a novel application of resurgence theory to the O(4) sigma model, extracting exact Stokes constants and formulating ambiguity-free trans-series.

Findings

Identification of Stokes constants and alien derivatives with exact expressions

Complete agreement between resurgence analysis and numerical solutions

High-precision perturbative coefficients up to 2000 terms

Abstract

We analyze the free energy of the integrable two dimensional O(4) sigma model in a magnetic field. We use Volin's method to extract high number (2000) of perturbative coefficients with very high precision. The factorial growth of these coefficients are regulated by switching to the Borel transform, where we perform several asymptotic analysis. High precision data allowed to identify Stokes constants and alien derivatives with exact expressions. These reveal a nice resurgence structure which enables to formulate the first few terms of the ambiguity free trans-series. We check these results against the direct numerical solution of the exact integral equation and find complete agreement.