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

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 a 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.

On exceptional QP-manifolds

“…For this the question is: what is {ξ M , ξ N }? For the string and the associated O(d, d)-covariant QP-manifold there is a natural definition, as discussed in section 3.2 and employed for example already in [56]:…”

“…These are based on the AKSZ-construction [49] and concrete connections to generalised geometry were used for example in [50][51][52]. In related contexts for O(d, d) generalised geometry in [53][54][55][56], supergeometric methods were applied. One aim of this article is to present a way to derive similar objects for p-branes from an underlying object, an E d(d) -covariant QP-manifold.…”