Torus bundles, automorphisms and T-duality

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.

Automated summary

In this paper, we reconsider some older constructions of T-duality based on automorphisms of the worldsheet operator algebra, and apply them in a modern context. Apart from special points, T-duality can be understood as a residual discrete gauge symmetry, and we discuss how to generalize this framework to geometric and non-geometric backgrounds. Additionally, an interesting algebraic structure is found along with its relationship with doubled geometry, as well as commenting on non-isometric T-duality in this context.