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

Pascal Grange·Sakura Schafer-Nameki
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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.

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Pascal Grange, Sakura Schafer-Nameki. 2006-09-27. T-duality with H-flux: non-commutativity, T-folds and G x G structure. https://doi.org/10.1016/j.nuclphysb.2007.02.003

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