Hamiltonian Loop Group Actions and T-Duality for group manifolds

Abstract

We carry out a Hamiltonian analysis of Poisson-Lie T-duality based on the loop geometry of the underlying phases spaces of the dual sigma and WZW models. Duality is fully characterized by the existence of equivariant momentum maps on the phase spaces such that the reduced phase space of the WZW model and a pure central extension coadjoint orbit work as a bridge linking both the sigma models. These momentum maps are associated to Hamiltonian actions of the loop group of the Drinfeld double on both spaces and the duality transformations are explicitly constructed in terms of these actions. Compatible dynamics arise in a general collective form and the resulting Hamiltonian description encodes all known aspects of this duality and its generalizations.

34 pages

References in corpus (2)

• Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models II: Nondiagonal metrics and dilaton puzzle
• The non-Abelian momentum map for Poisson-Lie symmetries on the chiral WZNW phase space

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• Integrable Systems and Poisson-Lie T-duality: a finite dimensional example
• Dirac approach to constrained submanifolds in a double loop group: from WZNW to Poisson-Lie $\sigma$-model
• Poisson-Lie T-Duality and non trivial monodromies
• Stratified Lie systems: Theory and applications