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.

arXiv comment37 pages, 5 figures, v3: typos corrected, Fig. 2 improved

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• Instantons, renormalons and the theta angle in integrable sigma models
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• When cold, dense quarks in 1+1 and 3+1 dimensions are not a Fermi liquid
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• All-order Resurgence from Complexified Path Integral in a Quantum Mechanical System with Integrability