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

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.