Poisson-Lie T-plurality as canonical transformation

TL;DR

This paper extends the classical Poisson-Lie T-duality framework to Poisson-Lie T-plurality, providing explicit formulas for canonical transformations that preserve the underlying Poisson structure.

Contribution

It introduces a generalized approach to Poisson-Lie T-plurality as a canonical transformation, including explicit transformation formulas and proof of bracket preservation.

Findings

Explicit formulas for canonical transformations under T-plurality

Proof of preservation of Poisson brackets and Hamiltonian density

Extension of T-duality to a pluralistic framework

Abstract

We generalize the prescription realizing classical Poisson-Lie T-duality as canonical transformation to Poisson-Lie T-plurality. The key ingredient is the transformation of left-invariant fields under Poisson-Lie T-plurality. Explicit formulae realizing canonical transformation are presented and the preservation of canonical Poisson brackets and Hamiltonian density is shown.