Non-geometric backgrounds, doubled geometry and generalised T-duality

TL;DR

This paper extends doubled geometry to include all coordinates, enabling a unified description of geometric, non-geometric, and duality-twisted string backgrounds, and explores their effective theories and world-sheet formulations.

Contribution

It introduces a fully doubled formalism for string backgrounds, generalizing previous approaches to encompass non-geometric and non-local geometries within a unified framework.

Findings

Formulation of a doubled space as a twisted torus from a group manifold.

Inclusion of non-geometric backgrounds and duality twists in the formalism.

Development of a world-sheet sigma model for these generalized backgrounds.

Abstract

String backgrounds with a local torus fibration such as T-folds are naturally formulated in a doubled formalism in which the torus fibres are doubled to include dual coordinates conjugate to winding number. Here we formulate and explore a generalisation of this construction in which all coordinates are doubled, so that the doubled space is a twisted torus, i.e. a compact space constructed from identifying a group manifold under a discrete subgroup. This incorporates reductions with duality twists, T-folds and a class of flux compactifications, together with the non-geometric backgrounds expected to arise from these through T-duality. It also incorporates backgrounds that are not even locally geometric, and suggests a generalisation of T-duality to a more general context. We discuss the effective field theory arising from such an internal sector, give a world-sheet sigma model formulation of string theory on such backgrounds and illustrate our discussion with detailed examples.