T-duality with H-flux: non-commutativity, T-folds and G x G structure

TL;DR

This paper explores T-duality with H-flux, revealing non-commutative geometries, T-folds, and generalized complex structures, and shows how non-geometric backgrounds relate to SU(3) x SU(3) structures and D-brane dynamics.

Contribution

It unifies various approaches to T-duality with flux, introduces the role of holomorphic Poisson bivectors, and connects non-geometry with generalized complex structures and SU(3) x SU(3) backgrounds.

Findings

Non-commutative torus fibrations are the open-string counterparts of T-folds.

Non-geometric T-duals are embedded into generalized complex six-tori.

Poisson bivectors encode non-commutativity and D-brane dimension variation.

Abstract

Various approaches to T-duality with NSNS three-form flux are reconciled. Non-commutative torus fibrations are shown to be the open-string version of T-folds. The non-geometric T-dual of a three-torus with uniform flux is embedded into a generalized complex six-torus, and the non-geometry is probed by D0-branes regarded as generalized complex submanifolds. The non-commutativity scale, which is present in these compactifications, is given by a holomorphic Poisson bivector that also encodes the variation of the dimension of the world-volume of D-branes under monodromy. This bivector is shown to exist in SU(3) x SU(3) structure compactifications, which have been proposed as mirrors to NSNS-flux backgrounds. The two SU(3)-invariant spinors are generically not parallel, thereby giving rise to a non-trivial Poisson bivector. Furthermore we show that for non-geometric T-duals, the Poisson bivector may not be decomposable into the tensor product of vectors.