From perturbative to non-perturbative in the O(4) sigma model

TL;DR

This paper investigates the transition from perturbative to non-perturbative regimes in the O(4) sigma model by analyzing high-order perturbative data and identifying exact non-perturbative contributions, confirming results through numerical solutions.

Contribution

It provides a detailed analysis of the resurgent trans-series in the O(4) sigma model, explicitly determining leading non-perturbative terms using integrability and high-order perturbative data.

Findings

Exact leading non-perturbative terms identified and verified.

High-order perturbative data obtained through integrability.

Complete agreement with numerical solutions of the integral equation.

Abstract

We study the resurgent trans-series for the free energy of the two-dimensional O(4) sigma model in a magnetic field. Exploiting integrability, we obtain very high-order perturbative data, from which we can explore non-perturbative sectors. We are able to determine exactly the leading real-valued exponentially small terms, which we check against the direct numerical solution of the exact integral equation, and find complete agreement.