Fermionic Coset Models as Topological Models

TL;DR

This paper demonstrates that certain fermionic coset models are topological quantum field theories, establishing their equivalence to 2D Abelian and non-Abelian BF systems through explicit calculations.

Contribution

It shows that fermionic realization of $G/H$ coset models can be interpreted as topological models, extending the understanding of their structure and relation to BF theories.

Findings

The $U(1)/U(1)$ model defines a Topological Quantum Field Theory.

The $G/G$ coset models are topological, confirmed by explicit computation.

Extension of 2D BF systems to non-Abelian symmetry is natural and consistent.

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.