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

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.