Hamiltonian Loop Group Actions and T-Duality for group manifolds

TL;DR

This paper provides a Hamiltonian framework for Poisson-Lie T-duality on group manifolds, using loop group actions and momentum maps to connect dual sigma and WZW models.

Contribution

It introduces a Hamiltonian analysis based on loop geometry, characterizing duality through equivariant momentum maps and explicit duality transformations.

Findings

Duality characterized by equivariant momentum maps.

Explicit construction of duality transformations.

Unified Hamiltonian description of Poisson-Lie T-duality.

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.