Super-Instantons and the Reliability of Perturbation Theory in Non-Abelian Models

TL;DR

This paper investigates how super-instantons influence the reliability of perturbation theory in non-Abelian models at low temperatures, revealing modifications to the beta function that persist even at large N.

Contribution

It demonstrates that super-instantons cause perturbation theory to deviate from standard results in non-Abelian models, affecting the beta function at order 1/β².

Findings

Super-instantons dominate low-temperature behavior in non-Abelian models.

Perturbation theory with super-instantons yields different Green's functions from standard predictions.

The beta function of O(N) models is modified by super-instantons, with effects persisting at large N.

Abstract

In dimension $D\leq 2$ the low temperature behavior of systems enjoying a continuous symmetry is dominated by super-instantons: classical configurations of arbitrarily low energy. Perturbation theory in the background of a super-instanton produces thermodynamic answers for the invariant Green's functions that differ from the standard ones, but only in non-Abelian models and only starting at $O(1/\beta^2)$. This effect modifies the $\beta$-function of the $O(N)$ models and persists in the large $N$ limit of the $O(N)$ models.