Resurgence and 1/N Expansion in Integrable Field Theories

Autor: Lorenzo Di Pietro, Marcos Mariño, Giacomo Sberveglieri, Marco Serone
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Zdroj: Journal of High Energy Physics, Vol 2021, Iss 10, Pp 1-56 (2021)
Druh dokumentu: article
ISSN: 1029-8479
DOI: 10.1007/JHEP10(2021)166
Popis: Abstract In theories with renormalons the perturbative series is factorially divergent even after restricting to a given order in 1/N, making the 1/N expansion a natural testing ground for the theory of resurgence. We study in detail the interplay between resurgent properties and the 1/N expansion in various integrable field theories with renormalons. We focus on the free energy in the presence of a chemical potential coupled to a conserved charge, which can be computed exactly with the thermodynamic Bethe ansatz (TBA). In some examples, like the first 1/N correction to the free energy in the non-linear sigma model, the terms in the 1/N expansion can be fully decoded in terms of a resurgent trans-series in the coupling constant. In the principal chiral field we find a new, explicit solution for the large N free energy which can be written as the median resummation of a trans-series with infinitely many, analytically computable IR renormalon corrections. However, in other examples, like the Gross-Neveu model, each term in the 1/N expansion includes non-perturbative corrections which can not be predicted by a resurgent analysis of the corresponding perturbative series. We also study the properties of the series in 1/N. In the Gross-Neveu model, where this is convergent, we analytically continue the series beyond its radius of convergence and show how the continuation matches with known dualities with sine-Gordon theories.
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