Superconformal Coset Equivalence from Level-Rank Duality

Abstract

We construct a one-to-one map between the primary fields of the N=2 superconformal Kazama-Suzuki models G(m,n,k) and G(k,n,m) based on complex Grassmannian cosets, using level-rank duality of Wess-Zumino-Witten models. We then show that conformal weights, superconformal U(1) charges, modular transformation matrices, and fusion rules are preserved under this map, providing strong evidence for the equivalence of these coset models.