Abstract
The four-dimensional N = 1 supergravity theories arising in compactifications of type IIA and type IIB on generalized orientifold backgrounds with background fluxes are discussed. The Kähler potentials are derived for reductions on SU ( 3 ) structure orientifolds and shown to consist of the logarithm of the two Hitchin functionals. These are functions of even and odd forms parameterizing the geometry of the internal manifold, the B-field and the dilaton. The superpotentials induced by background fluxes and the non-Calabi–Yau geometry are determined by a reduction of the type IIA and type IIB fermionic actions on SU ( 3 ) and generalized SU ( 3 ) × SU ( 3 ) manifolds. Mirror spaces of Calabi–Yau orientifolds with electric and part of the magnetic NS–NS fluxes are conjectured to be certain SU ( 3 ) × SU ( 3 ) structure manifolds. Evidence for this identification is provided by comparing the generalized type IIA and type IIB superpotentials.
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