N=2 gauged WZW models and the elliptic genus

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.