Flux compactifications, twisted tori and doubled geometry

TL;DR

This paper explores flux compactifications and T-duality in string theory using a doubled geometry approach, analyzing a six-dimensional model to connect various string backgrounds and their global properties.

Contribution

It provides a detailed six-dimensional example illustrating different string backgrounds via polarizations and extends the sigma model to include bundles over a base, enhancing the doubled geometry formalism.

Findings

Different polarizations yield diverse string backgrounds.

The extended sigma model describes target spaces as bundles, capturing more complex geometries.

Connections with gauged supergravity are established.

Abstract

In arXiv:0902.4032 [hep-th] an O(D,D)-covariant sigma model describing the embedding of a closed world-sheet into the 2D-dimensional twisted torus was proposed. Such sigma models provide a universal description of string theory with target spaces related by the action of T-duality. In this article a six-dimensional toy example is studied in detail. Different polarisations of the six-dimensional target space give different three-dimensional string backgrounds including a nilmanifold with H-flux, a T-fold with R-flux and a new class of T-folds. Global issues and connections with the doubled torus formalism are discussed. Finally, the sigma model introduced in arXiv:0902.4032 [hep-th], describing the embedding of a world-sheet into the doubled twisted torus, is generalised to one describing a target space which is a bundle of the doubled twisted torus over a base, allowing for a more complete description of the associated gauged supergravity from the world-sheet perspective to be given.