Poisson–Lie T-Duality¶for Quasitriangular Lie Bialgebras

Abstract:

We introduce a new 2-parameter family of sigma models exhibiting Poisson–Lie T-duality on a quasitriangular Poisson–Lie group G. The models contain previously known models as well as a new 1-parameter line of models having the novel feature that the Lagrangian takes the simple form , where the generalised metric E is constant (not dependent on the field u as in previous models). We characterise these models in terms of a global conserved G-invariance. The models on G=SU ₂ and its dual G ^* are computed explicitly. The general theory of Poisson–Lie T-duality is also extended, notably the reduction of the Hamiltonian formulation to constant loops as integrable motion on the group manifold. The approach also points in principle to the extension of T-duality in the Hamiltonian formulation to group factorisations D=G⋈M, where the subgroups need not be dual or connected to the Drinfeld double.