DUAL NON-ABELIAN DUALITY AND THE DRINFELD DOUBLE

The standard notion of the non-Abelian duality in string theory is generalized to the class of sigma-models admitting a Poisson-Lie-like symmetry. Such sigma-models can be associated with every Lie bialgebra (G,G). Within the enlarged class of the backgrounds the non-Abelian duality is a duality transformation in the proper sense of the word. It exchanges the roles of G and G and it can be interpreted as a symplectomorphism of the phase spaces of the mutually dual theories. We give explicit formulas for the non-Abelian duality transformation for any (G,G). The non-Abelian analogue of the Abelian modular space O(d,d;Z) consists of all maximally isotropic decompositions of the corresponding DrinfeId double.