Effective descriptions of branes on non-geometric tori

Abstract

We investigate the low-energy effective description of non-geometric compactifications constructed by T-dualizing two or three of the directions of a T^3 with non-vanishing H-flux. Our approach is to introduce a D3-brane in these geometries and to take an appropriate decoupling limit. In the case of two T-dualities, we find at low energies a non-commutative T^2 fibered non-trivially over an S^1. In the UV this theory is still decoupled from gravity, but is dual to a little string theory with flavor. For the case of three T-dualities, we do not find a sensible decoupling limit, casting doubt on this geometry as a low-energy effective notion in critical string theory. However, by studying a topological toy model in this background, we find a non-associative geometry similar to one found by Bouwknegt, Hannabuss, and Mathai.

22 pages, 4 figures, references added

References in corpus (3)

• T-duality for principal torus bundles
• D-branes in Nongeometric Backgrounds
• D6-branes and torsion

Cited by in corpus (7)

• Lectures on Nongeometric Flux Compactifications
• Toroidal Orientifolds in IIA with General NS-NS Fluxes
• NS-NS fluxes in Hitchin's generalized geometry
• On T-duality transformations for the three-sphere
• Towards mirror symmetry à la SYZ for generalized Calabi-Yau manifolds
• Backreacted T-folds and non-geometric regions in configuration space
• D-branes, KK-theory and duality on noncommutative spaces