Dual Non-Abelian Duality and the Drinfeld Double

Details Dual Non-Abelian Duality and the Drinfeld Double Dual Non-Abelian Duality and the Drinfeld Double

1995-02-20

arxiv.org/abs/hep-th/9502122v3

Phys.Lett.B351:455-462,1995

Physics

High Energy Physics

High Energy Physics - Theory

(misprint in the bialgebra condition corrected)

Scientific paper

10.1016/0370-2693(95)00451-P

The standard notion of the non-Abelian duality in string theory is generalized to the class of $\si$-models admitting `non-commutative conserved charges'. Such $\si$-models can be associated with every Lie bialgebra $(\cg ,\cgt)$ and they possess an isometry group iff the commutant $[\cgt,\cgt]$ is not equal to $\cgt$. Within the enlarged class of the backgrounds the non-Abelian duality {\it is} a duality transformation in the proper sense of the word. It exchanges the roles of $\cg$ and $\cgt$ 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 $(\cg,\cgt)$. The non-Abelian analogue of the Abelian modular space $O(d,d;{\bf Z})$ consists of all maximally isotropic decompositions of the corresponding Drinfeld double.

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