Torus Bundles, Automorphisms and T-Duality

TL;DR

This paper revisits classical T-duality constructions using automorphisms of the worldsheet algebra, extending the framework to include non-geometric backgrounds and exploring algebraic structures related to doubled geometry.

Contribution

It generalizes T-duality to non-geometric backgrounds beyond solutions of string theory, connecting automorphisms, algebraic structures, and doubled geometry.

Findings

Identifies an algebraic structure related to T-duality.

Extends T-duality framework to non-geometric backgrounds.

Discusses non-isometric T-duality in a modern context.

Abstract

We reconsider some older constructions of T-duality, based on automorphisms of the worldsheet operator algebra, in a modern context. It has been long known that at special points in the moduli space of torus compactifications, the target space gauge symmetry may be enhanced. Away from such points the symmetry is broken and T-duality may be understood as a residual discrete gauge symmetry that survives this breaking. Drawing on work on connections over the space of string backgrounds, we discuss how to generalise this framework for T-duality to geometric and non-geometric backgrounds that are not full solutions of string theory, but may play an important role in exact backgrounds. Along the way we find an interesting algebraic structure and discuss its relationship with doubled geometry. We comment on non-isometric T-duality in this context.