Comment on "Superinstantons and the Reliability of Perturbation Theory in Non-Abelian Models"

TL;DR

This paper critiques a recent claim that superinstantons modify the perturbative beta-function in 2D non-linear sigma-models, showing that infra-red singularities and operator analysis prevent such modifications, reaffirming the validity of standard perturbation theory.

Contribution

The paper clarifies that superinstantons do not alter the beta-function due to infra-red singularities and operator effects, countering previous claims.

Findings

Infra-red singularities occur beyond three loops in superinstanton backgrounds.

Singular operators in the OPE account for the infra-red effects.

The beta-function remains unchanged when these operators are considered.

Abstract

In a recent letter (hep-lat/9311019) A. Patrascioiu and E. Seiler argued that when taking into account "superinstantons configurations" the perturbative expansion and the beta-function of the two-dimensional non-linear sigma-model are modified at two loops order. I point out that: (1) perturbation theory in a superinstanton background is infra-red singular beyond three loops; (2) the new infra-red singular terms, which change the two loop terms, come from singular operators - describing superinstanton insertions - in the OPE; (3) taking into account these operators, the beta-function is not modified. Therefore the results of Patrascioiu and Seiler do not contradict perturbation theory.