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

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.

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References in corpus (3)

• Renormalization Theory for Interacting Crumpled Manifolds
• Super-Instantons and the Reliability of Perturbation Theory in Non-Abelian Models
• Super-Instantons in Gauge Theories and Troubles with Perturbation Theory

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• Super-Instantons, Perfect Actions, Finite Size Scaling and the Continuum Limit
• Reply to David's Comment on ``Superinstantons and the Reliability of Perturbation Theory in Non-Abelian Models''
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• Exponential corrections to low-temperature expansion of 2D non-abelian models