Patching DFT, T-duality and Gerbes

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.

minor changes, references added

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Cited by in corpus (7)

• Non-geometric backgrounds in string theory
• The Geometry, Branes and Applications of Exceptional Field Theory
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• Exotic branes in Exceptional Field Theory: the SL(5) duality group
• Born Sigma-Models for Para-Hermitian Manifolds and Generalized T-Duality
• Global Double Field Theory is Higher Kaluza-Klein Theory
• The puzzle of global Double Field Theory: open problems and the case for a Higher Kaluza-Klein perspective