1999/06/07 by E. J. Beggs, Beggs, E. J., S. Majid +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #hep-th #math.QA
paper · pdf · doi:10.48550/arxiv.math/9906040
42 pages Latex, no figures
arxiv created 1999/06/07 · arxiv updated 2009/11/30
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 L=E(u-1u+,u-1u-) 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=SU2 and its dual G^⋆ are computed explicitly. The general theory of Poisson-Lie T-duality is also extended; we develop the Hamiltonian formulation and the reduction for constant loops to integrable motion on the group manifold. Finally, we generalise T-duality in the Hamiltonian formulation to group factorisations D=G\dcross M where the subgroups need not be dual or even have the same dimension and need not be connected to the Drinfeld double or to Poisson structures.