2006/09/27 by Pascal Grange, Sakura Schafer-Nameki, Sakura Schäfer‐Nameki
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Commutative property #Cosmology and Gravitation Theories #Dual polyhedron #Geometry #Holomorphic function #Mathematical physics #Mathematics #Monodromy #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Pure mathematics #String theory #T-duality #Torus #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2007.02.003
published as Nucl.Phys.B770:123-144,2007 · 25 pages, LaTeX; v2: typos corrected, references added
arxiv created 2006/09/27 · openalex publication_date 2007/02/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.