Ramond-Ramond Cohomology and O(D,D) T-duality

TL;DR

This paper reformulates superstring effective actions within double field theory, incorporating Ramond-Ramond potentials as O(D,D) spinors, revealing cohomological structures and T-duality transformations that exchange IIA and IIB supergravities.

Contribution

It introduces a covariant framework for R-R potentials as bi-fundamental spinors in double field theory, elucidating their cohomological structure and T-duality behavior.

Findings

R-R potentials are incorporated as O(D,D) spinors.

Cohomological structure of R-R field strength identified.

T-duality exchanges IIA and IIB supergravities via chirality flip.

Abstract

In the name of supersymmetric double field theory, superstring effective actions can be reformulated into simple forms. They feature a pair of vielbeins corresponding to the same spacetime metric, and hence enjoy double local Lorentz symmetries. In a manifestly covariant manner --with regard to O(D,D) T-duality, diffeomorphism, B-field gauge symmetry and the pair of local Lorentz symmetries-- we incorporate R-R potentials into double field theory. We take them as a single object which is in a bi-fundamental spinorial representation of the double Lorentz groups. We identify cohomological structure relevant to the field strength. A priori, the R-R sector as well as all the fermions are O(D,D) singlet. Yet, gauge fixing the two vielbeins equal to each other modifies the O(D,D) transformation rule to call for a compensating local Lorentz rotation, such that the R-R potential may turn into an O(D,D) spinor and T-duality can flip the chirality exchanging type IIA and IIB supergravities.