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Wiener-Hopf solution of the free energy TBA problem and instanton sectors in the O(3) sigma model
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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.
Forward citations
Cited by 2 Pith papers
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The complete trans-series for conserved charges in integrable field theories
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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From Fredholm Determinants to AdS/CFT Observables: A Universal Strong-Coupling Framework
The O(6) mass gap's strong-coupling trans-series is generated from Fredholm-determinant data via a conjectured alien calculus, yielding an all-orders relation to the cusp anomalous dimension.
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