Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles

Abstract

A duality invariant first order action is constructed on the loop group of a Drinfeld double. It gives at the same time the description of both of the pair of $\sigma$-models related by Poisson-Lie T-duality. Remarkably, the action contains a WZW-term on the Drinfeld double not only for conformally invariant $\si$-models. The resulting actions of the models from the dual pair differ just by a total derivative corresponding to an ambiguity in specifying a two-form whose exterior derivative is the WZW three-form. This total derivative is nothing but the Semenov-Tian-Shansky symplectic form on the Drinfeld double and it gives directly a generating function of the canonical transformation relating the $\si$-models from the dual pair.

15 pages, LaTeX

References in corpus (4)

• Duality and Dilaton
• Poisson-Lie T-duality
• Poisson-Lie T-Duality: the Path-Integral Derivation
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