nLab differential T-duality

Idea

Analogous to how topological T-duality describes the aspects of T-duality that are not related to the pseudo-Riemannian metric and the background gauge field, differential T-duality still ignores the metric, but takes the background Kalb-Ramond field and its effect on the RR-fields into account: it is a refinement of topological T-duality from cohomology to differential cohomology.

This is also called geometric T-duality (KahleValentino), though this is a slight misnomer, since present technnology for the differential refinement does not take the metric into account.

Definition

(KahleValentino=.

Formulation by twisted differential $\mathbf{c}$-structures

We discuss here how the notion of differential T-duality pairs is a special case of the notion of twisted differential c-structures.

(…)

for the moment see the remarks included in T-Duality and Differential K-Theory

Related concepts

• T-duality

  • topological T-duality

  • differential T-duality

• Bn-geometry, generalized complex geometry

References

The first proposal for a description of differential T-duality is

• Alexander Kahle, Alessandro Valentino, T-Duality and Differential K-Theory

A review is in section 7.4 of

• Ulrich Bunke, Thomas Schick, Differential K-theory. A survey (arXiv:1011.6663).