Hitchin Functionals in N=2 Supergravity

Abstract

We consider type II string theory in space-time backgrounds which admit eight supercharges and can be characterized by the existence of an SU(3) x SU(3) structure. We show that the couplings of such backgrounds strongly resemble the couplings of four-dimensional N=2 supergravities and precisely coincide with the N=2 couplings after an appropriate Kaluza-Klein reduction. Specifically we show that the moduli space of metrics admits a special Kahler geometry with Kahler potentials given by the Hitchin functionals. Furthermore we explicitly compute the N=2 version of the superpotential from the transformation law of the gravitinos, and find its N=1 counterpart.