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.

Resurgence and 1/N Expansion in Integrable Field Theories / Di Pietro, Lorenzo; Mariño, Marcos; Sberveglieri, Giacomo; Serone, Marco. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2021:10(2021), pp. 1-55. [10.1007/jhep10(2021)166]

Resurgence and 1/N Expansion in Integrable Field Theories

Di Pietro, Lorenzo
;
Sberveglieri, Giacomo;Serone, Marco
2021

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.
2021
10
1
55
166
10.1007/jhep10(2021)166
https://arxiv.org/abs/2108.02647
Di Pietro, Lorenzo; Mariño, Marcos; Sberveglieri, Giacomo; Serone, Marco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/128530
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