On the classical connection between the WZWN model and topological gauge theories with boundaries

TL;DR

This paper demonstrates a classical equivalence between the WZWN model and a combination of BF and Chern-Simons theories with boundaries, using non-Abelian T-duality techniques, and explores different dual theories based on Lie algebra choices.

Contribution

It establishes a classical connection between the WZWN model and topological gauge theories, highlighting the role of boundary terms and duality transformations.

Findings

WZWN model is classically equivalent to BF and Chern-Simons theories with boundary terms.

Different dual theories emerge depending on solutions to consistency conditions.

Three-dimensional gravity arises only when the BF term is neglected for specific Lie algebras.

Abstract

It is shown, at the level of the classical action, that the Wess-Zumino-Witten-Novikov model is equivalent to a combined BF theory and a Chern-Simons action in the presence of a unique boundary term. This connection relies on the techniques of non-Abelian T-duality in non-linear sigma models. We derive some consistency conditions whose various solutions lead to different dual theories. Particular attention is paid to the cases of the Lie algebras SO(2,1) and SO(2,1)*SO(2,1). These are shown to yield three dimensional gravity only if the BF term is ignored.