Poisson-Lie Sigma Models on Drinfel'd double
Differential Geometry
2013-01-14 v1 High Energy Physics - Theory
Abstract
Poisson sigma models represent an interesting use of Poisson manifolds for the construction of a classical field theory. Their definition in the language of fibre bundles is shown and the corresponding field equations are derived using a coordinate independent variational principle. The elegant form of equations of motion for so called Poisson-Lie groups is derived. Construction of the Poisson-Lie group corresponding to a given Lie bialgebra is widely known only for coboundary Lie bialgebras. Using the adjoint representation of Lie group and Drinfel'd double we show that Poisson-Lie group can be constructed for general Lie bialgebra.
Cite
@article{arxiv.1211.0901,
title = {Poisson-Lie Sigma Models on Drinfel'd double},
author = {Jan Vysoky and Ladislav Hlavaty},
journal= {arXiv preprint arXiv:1211.0901},
year = {2013}
}