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

\'Arp\'ad Heged\H{u}s; J\'anos Balog; Michael C. Abbott; Zolt\'an Bajnok

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

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arxiv 2011.09897 v3 pith:JHKGOFVK submitted 2020-11-19 hep-th

Michael C. Abbott , Zoltán Bajnok , János Balog , Árpád Hegedűs This is my paper · ORCID

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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.

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The complete trans-series for conserved charges in integrable field theories
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A unified Wiener-Hopf construction gives all-order trans-series for conserved charges in O(N), SU(N), Lieb-Liniger, Gaudin-Yang and capacitor models, with numerically checked Borel resummation.

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