Effective descriptions of branes on non-geometric tori

TL;DR

This paper explores the low-energy effective descriptions of non-geometric string compactifications involving T-duality, revealing non-commutative and non-associative geometries and their relation to little string theories.

Contribution

It introduces a D3-brane approach to analyze non-geometric T-dual backgrounds, uncovering non-commutative and non-associative structures and discussing their decoupling limits.

Findings

Non-commutative T^2 fibered over S^1 in two T-dualities case

Decoupled UV theory dual to little string theory with flavor

No sensible decoupling limit found for three T-dualities case

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.