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

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. (C) 2021 The Authors. Published by Elsevier B.V.

Automated summary

In this study, we investigate the resurgent trans-series for the free energy of the two-dimensional O(4) sigma model in a magnetic field. By exploiting integrability, very high-order perturbative data is obtained, allowing exploration of non-perturbative sectors. Leading real-valued exponentially small terms are determined exactly and confirmed against direct numerical solutions, showing complete agreement.