Resurgence in the O(4) sigma model
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.
Cite
@article{arxiv.2011.12254,
title = {Resurgence in the O(4) sigma model},
author = {Michael C. Abbott and Zoltán Bajnok and János Balog and Árpád Hegedűs and Saeedeh Sadeghian},
journal= {arXiv preprint arXiv:2011.12254},
year = {2023}
}
Comments
37 pages, 5 figures, v3: typos corrected, Fig. 2 improved