Stringy unification of type IIA and IIB supergravities under [formula omitted][formula omitted] supersymmetric double field theory

Imtak Jeon,Kanghoon Lee,Jeong-Hyuck Park,Yoonji Suh

doi:10.1016/j.physletb.2013.05.016

Abstract

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)×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.

Highlights

We introduce master ‘semi-covariant’ derivative DA = ∂A + ΓA + ΦA + Φ A
General torsionful conection, ΓCAB = Γ0CAB + ∆CAB, As in SUGRA, the torsion can be constructed from the bi-spinorial objects, e.g. ργBCψA, ψBγAψC, ργABCρ, ψpγABCψp, where we set ψA = VApψp, γA = VApγp
Since the two zehnbeins correspond to the same spacetime metric, they must be related by a Lorentz rotation, (e−1 ̄e)pp(e−1 ̄e)qqηpq = −ηpq

Summary

Symmetries of SDFT

DFT-diffeomorphism (generalized Lie derivative) Diffeomorphism B-field gauge symmetry 2. General torsionful conection , ΓCAB = Γ0CAB + ∆CAB , As in SUGRA, the torsion can be constructed from the bi-spinorial objects, e.g. ργBCψA , ψBγAψC , ργABCρ , ψ ̄pγABCψp , where we set ψA = VApψp, γA = VApγp. For Spin(1, D−1)L × Spin(D−1, 1)R tensors: DpTq , DpTp , DpDpTq , DpDpTq , where we set. The field strength of the R-R potential, Cαα , is defined by F := D+0 C. This is Not covariant tensor, but contracting with projection operators, we can obtain covariant quatities. Assuming that the upper half blocks are non-degenerate, the double-vielbein takes the most general form,. This reduces (S)DFT to generalized geometry Hitchin; Grana, Minasian, Petrini, Waldram

Unification of type IIA and IIB SUGRAs

Diagonal gauge fixing and Reduction to SUGRA

Summary