Gauge Symmetry, T-Duality and Doubled Geometry

TL;DR

This paper explores the formulation of string theory compactifications with T-duality twists using doubled geometry, proposing a framework that includes non-geometric backgrounds and extends the concept of T-duality.

Contribution

It introduces a doubled space framework incorporating T-duality on the base circle, including dual coordinates, and relates to Drinfel'd doubles for non-geometric backgrounds.

Findings

Calculated gauge algebra of reduced theories with T-duality twists

Formulated doubled torus bundle over a circle for string backgrounds

Proposed extension to include T-duality on the base circle with dual coordinates

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.