Super-Instantons in Gauge Theories and Troubles with Perturbation Theory

TL;DR

This paper explores super-instantons in non-Abelian gauge theories, revealing their role in causing perturbation theory failures at short distances, especially at order 1/beta^2, highlighting fundamental issues in theoretical predictions.

Contribution

It identifies the existence of super-instantons in gauge theories and links them to perturbation theory ambiguities, providing new insights into non-Abelian model behaviors.

Findings

Super-instantons have zero energy in the thermodynamic limit.

Perturbation theory can fail to produce unique results at O(1/beta^2).

Failures are specific to non-Abelian gauge theories.

Abstract

In gauge theories with continuous groups there exist classical solutions whose energy vanishes in the thermodynamic limit (in any dimension). The existence of these super-instantons is intimately related to the fact that even at short distances perturbation theory can fail to produce unique results. This problem arises only in non-Abelian models and only starting at O(1/beta^2).