Renormalons in integrable field theories

TL;DR

This paper analyzes the high-order behavior of perturbative series in two-dimensional integrable field theories, providing analytic results and evidence that renormalons control the series' divergence, with implications for understanding non-perturbative effects.

Contribution

It extends previous work by deriving high-order perturbative expansions and analyzing renormalon effects in various integrable models, including supersymmetric extensions.

Findings

Perturbative series are controlled by renormalons.

High-order expansions are computed analytically.

Next-to-leading corrections involve beta function coefficients.

Abstract

In integrable field theories in two dimensions, the Bethe ansatz can be used to compute exactly the ground state energy in the presence of an external field coupled to a conserved charge. We generalize previous results by Volin and we extract analytic results for the perturbative expansion of this observable, up to very high order, in various asymptotically free theories: the non-linear sigma model and its supersymmetric extension, the Gross--Neveu model, and the principal chiral field. We study the large order behavior of these perturbative series and we give strong evidence that, as expected, it is controlled by renormalons. Our analysis is sensitive to the next-to-leading correction to the asymptotics, which involves the first two coefficients of the beta function.