Gauged WZW models and Non-abelian duality

TL;DR

This paper explores gauged WZW models based on non-semi-simple algebras, demonstrating their relation to non-abelian duality transformations and showing how certain limits connect these models to dualized WZW actions.

Contribution

It provides explicit expressions for these models, generalizes them, and establishes their equivalence to non-abelian duality transformations, expanding understanding of dualities in non-semi-simple algebra contexts.

Findings

Gauged WZW models on non-semi-simple algebras are equivalent to non-abelian duality transformations.

A limit of the coset model reproduces the dualized WZW action for a subgroup.

The paper generalizes the construction of gauged WZW models and clarifies their duality properties.

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 $H$.