Stringy Unification of Type IIA and IIB Supergravities under N=2 D=10 Supersymmetric Double Field Theory

To the full order in fermions, we construct D=10 type II supersymmetric double field theory. We spell the precise N=2 supersymmetry transformation rules as for 32 supercharges. The constructed action unifies type IIA and IIB supergravities in a manifestly covariant manner with respect to O(10,10) T-duality and a pair of local Lorentz groups, or Spin(1,9) times Spin(9,1), besides the usual general covariance of supergravities or the generalized diffeomorphism. While the theory is unique, the solutions are twofold. Type IIA and IIB supergravities are identified as two different types of solutions rather than two different theories.

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

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.