# nLab T-fold

### Context

#### Riemannian geometry

Riemannian geometry

duality

# Contents

## Idea

A T-fold (Hull 04) is supposed to be a kind of space that locally looks like a Riemannian manifold equipped with a B-field, but which is is glued together from these not just by diffeomorphisms but also by T-duality transformations along some torus fibers.

The idea is that a T-fold is a target space for a string sigma-model that is only locally a Riemannian manifold but globally a more general kind of geometry. In the literature sometimes the term non-geometric backgrounds is used for such “generalized geometric” backgrounds.

It is expected that T-folds should have a description in terms of spaces that locally are fiber products of one torus fiber bundle with its T-dual. (One proposed formalization is that these are the total spaces of principal 2-bundles for the T-duality 2-group).

One may then consider local field theory on these double torus fibrations, and this is, or is closely related to, what is called double field theory (Hull 06).

## References

The idea was originally introduced in

The relation to double field theory goes back to

Further developments are in

A precise global definition of T-folds as principal 2-bundles for the T-duality 2-group described in the nLab entry T-Duality and Differential K-Theory is given in

• Thomas Nikolaus, T-Duality in K-theory and elliptic cohomology, talk at String Geometry Network Meeting, Feb 2014, ESI Vienna (website)

Revised on April 4, 2017 03:02:10 by Urs Schreiber (78.47.168.108)