Affine Poisson and affine quasi-Poisson T-duality

TL;DR

This paper extends Poisson-Lie T-duality using affine Poisson groups and introduces affine quasi-Poisson groups, creating a broader T-duality framework compatible with renormalization group flow.

Contribution

It introduces affine quasi-Poisson groups and develops a more general T-duality framework based on affine Poisson geometry.

Findings

Affine Poisson groups generalize Poisson-Lie groups.

Affine quasi-Poisson groups lead to a new T-duality framework.

The new T-duality is compatible with renormalization group flow.

Abstract

We generalize the Poisson-Lie T-duality by making use of the structure of the affine Poisson group which is the concept introduced some time ago in Poisson geometry as a generalization of the Poisson-Lie group. We also introduce a new notion of an affine quasi-Poisson group and show that it gives rise to a still more general T-duality framework. We establish for a class of examples that this new T-duality is compatible with the renormalization group flow.