Patching DFT, T-duality and Gerbes

TL;DR

This paper clarifies the relationship between T-duality coordinates, Double Field Theory, and gerbes, showing that T-duality angular dual coordinates cannot be directly identified with DFT dual coordinates and proposing a new geometric interpretation involving C-spaces.

Contribution

It demonstrates that T-duality angular coordinates have non-trivial transition functions and are not equivalent to DFT dual coordinates, proposing a C-space framework for T-dual spaces.

Findings

T-duality angular dual coordinates have non-trivial transition functions.

DFT coordinates can be identified with C-space coordinates.

T-dual spaces are subspaces of gerbes in C-space.

Abstract

We clarify the role of the dual coordinates as described from the perspectives of the Buscher T-duality rules and Double Field Theory. We show that the T-duality angular dual coordinates cannot be identified with Double Field Theory dual coordinates in any of the proposals that have been made in the literature for patching the doubled spaces. In particular, we show with explicit examples that the T-duality angular dual coordinates can have non-trivial transition functions over a spacetime and that their identification with the Double Field Theory dual coordinates is in conflict with proposals in which the latter remain inert under the patching of the B-field. We then demonstrate that the Double Field Theory coordinates can be identified with some C-space coordinates and that the T-dual spaces of a spacetime are subspaces of the gerbe in C-space. The construction provides a description of both the local $O(d,d)$ symmetry and the T-dual spaces of spacetime.