Effective descriptions of branes on non-geometric tori

TL;DR

The paper investigates low-energy descriptions of non-geometric compactifications arising from T-dualizing a $T^3$ with $H$-flux by embedding a D3-brane and taking a decoupling limit. It shows that the $Q$-space yields a field of non-commutative tori fibered over $S^1$, with a position-dependent Morita parameter and a UV completion to little string theory with flavor, decoupled from gravity; in contrast, the $R$-space does not admit a clean decoupled EFT, though a non-associative product emerges in toy/topological models and appears linked to non-geometric extensions of NC geometry. The work highlights Morita duality and non-associative algebras as concrete structures encoding non-geometricity, and addresses backreaction via a smeared NS5-brane background to assess the viability of these geometries as consistent low-energy descriptions. It also points to a potential role for Poisson–WZ type topological models in realizing the algebraic aspects beyond the confines of critical string theory.

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.