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

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.

1+37 pages, no figure; Structure reorganized, References added, To appear in JHEP. cf. Gong Show of Strings 2012 (http://wwwth.mpp.mpg.de/members/strings/strings2012/strings_files/program/Talks/Thursday/Gongshow/Lee.pdf)

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• Double Field Theory
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• Generalized Geometry and M theory
• Differential geometry with a projection: Application to double field theory
• On non-abelian T-dual geometries with Ramond fluxes
• Gauged Double Field Theory
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• Generalized non-supersymmetric flux vacua
• Smeared versus localised sources in flux compactifications
• Double field formulation of Yang-Mills theory
• E11, generalised space-time and IIA string theory
• T-duality in Ramond-Ramond backgrounds

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