N=4 Superconformal Algebras and Gauged WZW Models

TL;DR

This paper extends Witten's work on supersymmetric gauged WZW models, showing that under specific conditions these models exhibit N=4 superconformal symmetry, and relates them to maximal N=4 superconformal algebras.

Contribution

It generalizes the conditions for N=4 superconformal invariance in gauged WZW models and connects these models to maximal N=4 superconformal algebras.

Findings

Gauged WZW models over G×U(1) are N=4 superconformal if G/H×SU(2) is quaternionic symmetric.

Reformulation of maximal N=4 superconformal algebras with SU(2)×SU(2)×U(1) symmetry.

Expected quantization yields unitary realizations of maximal N=4 superconformal algebras.

Abstract

As shown by Witten the N=1 supersymmetric gauged WZW model based on a group G has an extended N=2 supersymmetry if the gauged subgroup H is so chosen that G/H is Kahler. We extend Witten's result and prove that the N=1 supersymmetric gauged WZW models over G X U(1) are actually invariant under N=4 superconformal transformations if the gauged subgroup H is such that G/HXSU(2) is a quaternionic symmetric space. A previous construction of "maximal" N=4 superconformal algebras with SU(2)XSU(2)XU(1) symmetry is reformulated and further developed so as to relate them to the N=4 gauged WZW models. Based on earlier results we expect the quantization of N=4 gauged WZW models to yield the unitary realizations of maximal N=4 superconformal algebras provided by this construction.