A QP perspective on topology change in Poisson-Lie T-duality

TL;DR

This paper presents a novel framework for understanding Poisson-Lie T-duality using QP manifolds, revealing new insights into topological and non-abelian dualities through symplectic reductions and canonical transformations.

Contribution

It introduces a QP manifold approach to topological and Poisson-Lie T-duality, connecting dualities with symplectic reductions and Fourier-Mukai transformations.

Findings

Duality mediated by a QP-manifold on doubled space

Symplectic reductions yield dual theories

Canonical transformations suggest Fourier-Mukai interpretation

Abstract

We describe topological T-duality and Poisson-Lie T-duality in terms of QP (differential graded symplectic) manifolds and their canonical transformations. Duality is mediated by a QP-manifold on doubled non-abelian "correspondence" space, from which we can perform mutually dual symplectic reductions, where certain canonical transformations play a vital role. In the presence of spectator coordinates, we show how the introduction of "bibundle" structure on correspondence space realises changes in the global fibration structure under Poisson-Lie duality. Our approach can be directly translated to the worldsheet to derive dual string current algebras. Finally, the canonical transformations appearing in our reduction procedure naturally suggest a Fourier-Mukai integral transformation for Poisson-Lie T-duality.