N=2 gauged WZW models and the elliptic genus

TL;DR

This paper computes the elliptic genus for N=2 gauged WZW models, providing evidence for their relationship with N=2 minimal models and confirming previous results through path integral methods.

Contribution

It offers the first calculation of the elliptic genus for N=2 gauged WZW models, connecting them to minimal models via explicit path integral evaluation.

Findings

Elliptic genus matches that of N=2 minimal models

Confirms conjectured relationship between gauged WZW and minimal models

Validates previous character-based calculations

Abstract

Witten recently gave further evidence for the conjectured relationship between the $A$ series of the $N=2$ minimal models and certain Landau-Ginzburg models by computing the elliptic genus for the latter. The results agree with those of the $N=2$ minimal models, as can be calculated from the known characters of the discrete series representations of the $N=2$ superconformal algebra. The $N=2$ minimal models also have a Lagrangian representation as supersymmetric gauged WZW models. We calculate the elliptic genera, interpreted as a genus one path integral with twisted boundary conditions, for such models and recover the previously known result.