Level-Rank Duality of WZW Theories and Isomorphisms of N = 2 Coset Models

Abstract

Mappings between certain infinite series of N = 2 superconformal coset models are constructed. They make use of level-rank dualities for B, C, and D type WZW theories, which are described in some detail. The WZW level-rank dualities do not constitute isomorphisms of the theories; for example, for B and D type WZW theories only simple current orbits rather than individual primary fields are mapped onto each other. Nevertheless they lead to level-rank dualities of N = 2 coset models that preserve the conformal field theory properties in such a manner that the coset models related by duality are expected to be, in fact, isomorphic as conformal field theories; in particular, the representation of the modular group on the characters and the ground states of the Ramond sector are shown to coincide. The construction also gives some further insight into the nature of the resolution of field identification fixed points of coset theories.