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arXiv · 2404.07621

Wiener-Hopf solution of the free energy TBA problem and instanton sectors in the O(3) sigma model

Zoltán Bajnok·János Balog·István Vona
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Abstract

Perturbation theory in asymptotically free quantum field theories is asymptotic. The factorially growing perturbative coefficients carry information about non-perturbative corrections, which can be related to renormalons and instantons. Using the Wiener-Hopf technique we determine the full analytic solution for the free energy density in the two dimensional $O(N)$ sigma models. For $N>3$ there are no instantons, and we found that the perturbative series carries all the information about the non-perturbative corrections. However, in the $O(3)$ case, we identify several non-perturbative sectors that are not related to the asymptotics of the perturbative series. The number of sectors depends on the observables: for the ground-state energy density we identify three sectors, which we attribute to instantons. For the free energy density in the running perturbative coupling we found infinitely many sectors.

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Zoltán Bajnok, János Balog, István Vona. 2024-12-05. Wiener-Hopf solution of the free energy TBA problem and instanton sectors in the O(3) sigma model. https://arxiv.org/abs/2404.07621

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