Gauge Symmetry, T-Duality and Doubled Geometry

TL;DR

The paper tackles how gauge symmetries and T-duality twists in string compactifications generate geometric and non-geometric backgrounds, and proposes a unified doubled-geometry framework. It develops the $O(d,d)$-twisted reduction, derives the corresponding gauge algebra, and constructs a doubled space ${\cal X}$ as the group manifold of the gauge group, extending to a doubled base to accommodate base T-duality. By organizing fluxes into $f$, $H$, $Q$, and $R$-types within this group-theoretic picture, it provides geometric interpretations for both T-folds and R-flux backgrounds and outlines a path to lifting these gaugings to full string theory. The approach clarifies how dualities act, offering a cohesive description of non-geometric backgrounds and their global realization via a doubled group ${\cal G}$ and cosets ${\cal G}/\Gamma$.

Abstract

String compactifications with T-duality twists are revisited and the gauge algebra of the dimensionally reduced theories calculated. These reductions can be viewed as string theory on T-fold backgrounds, and can be formulated in a `doubled space' in which each circle is supplemented by a T-dual circle to construct a geometry which is a doubled torus bundle over a circle. We discuss a conjectured extension to include T-duality on the base circle, and propose the introduction of a dual base coordinate, to give a doubled space which is locally the group manifold of the gauge group. Special cases include those in which the doubled group is a Drinfel'd double. This gives a framework to discuss backgrounds that are not even locally geometric.