Poisson-Lie Sigma Models on Drinfel'd double

TL;DR

This paper explores Poisson sigma models on Poisson-Lie groups, deriving their equations of motion and providing a general construction method for Poisson-Lie groups from Lie bialgebras using Drinfel'd doubles.

Contribution

It introduces a coordinate-independent formulation of Poisson sigma models and extends the construction of Poisson-Lie groups to general Lie bialgebras beyond coboundary cases.

Findings

Derived equations of motion for Poisson-Lie sigma models.

Presented a general construction method for Poisson-Lie groups from Lie bialgebras.

Extended known constructions to non-coboundary Lie bialgebras.

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.