Fermionic Coset Models as Topological Models

Abstract

By considering the fermionic realization of $G/H$ coset models, we show that the partition function for the $U(1)/U(1)$ model defines a Topological Quantum Field Theory and coincides with that for a 2-dimensional Abelian BF system. In the non-Abelian case, we prove the topological character of $G/G$ coset models by explicit computation, also finding a natural extension of 2-dimensional BF systems with non-Abelian symmetry.