Gauged WZW models and Non-abelian duality

Abstract

We consider WZW models based on the non-semi-simple algebras that they were recently constructed as contractions of corresponding algebras for semi-simple groups. We give the explicit expression for the action of these models, as well as for a generalization of them, and discuss their general properties. Furthermore we consider gauged WZW models based on these non-semi-simple algebras and we show that there are equivalent to non-abelian duality transformations on WZW actions. We also show that a general non-abelian duality transformation can be thought of as a limiting case of the non-abelian quotient theory of the direct product of the original action and the WZW action for the symmetry gauge group $H$. In this action there is no Lagrange multiplier term that constrains the gauge field strength to vanish. A particular result is that the gauged WZW action for the coset $(G_k \otimes H_l)/H_{k+l}$ is equivalent, in the limit $l\to \infty$, to the dualized WZW action for $G_k$ with respect to the subgroup $H$.