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Hamiltonian loop group actions and T-duality for group manifolds

Authors
Journal
Journal of Geometry and Physics
0393-0440
Publisher
Elsevier
Publication Date
Volume
56
Issue
7
Identifiers
DOI: 10.1016/j.geomphys.2005.06.006
Keywords
  • Poisson-Lie T-Duality
  • Hamiltonian Loop Group Actions
  • Dressing Actions
  • Momentum Maps
  • Collective Hamiltonians
Disciplines
  • Mathematics

Abstract

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.

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