Gauged WZW models and non-Abelian duality

We consider WZW models based on the non-semi-simple algebras that were recently constructed as contractions of corresponding algebras for semisimple 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 they 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 (${\mathit{G}}_{\mathit{k}}$⊗${\mathit{H}}_{\mathit{l}}$)/${\mathit{H}}_{\mathit{k}+\mathit{l}}$ becomes in a certain limit, involving l→∞, the dualized WZW action for ${\mathit{G}}_{\mathit{k}}$ with respect to the subgroup H.