Anomalous Dimensions in Deformed WZW Models on Supergroups

TL;DR

This paper analyzes how certain deformations of WZW models on supergroups affect the anomalous dimensions of operators, providing exact formulas and higher-loop calculations relevant for understanding dualities in conformal field theories.

Contribution

It derives an all-orders formula for anomalous dimensions in deformed WZW models on supergroups, extending previous perturbative results and offering insights into non-perturbative dualities.

Findings

Exact all-orders formula for anomalous dimensions

3-loop calculations of 2-point functions

Identification of supergroups preserving conformal invariance

Abstract

We investigate a class of current-current, Gross-Neveu like, perturbations of WZW models in which the full left-right affine symmetry is broken to the diagonal global algebra only. Our analysis focuses on those supergroups for which such a perturbation preserves conformal invariance. A detailed calculation of the 2-point functions of affine primary operators to 3-loops is presented. Furthermore, we derive an exact formula for the anomalous dimensions of a large subset of fields to all orders in perturbation theory. Possible applications of our results, including the study of non-perturbative dualities, are outlined.