Hitchin Functionals in N=2 Supergravity

TL;DR

This paper explores the geometric structures of type II string theory backgrounds with eight supercharges, revealing that their moduli space and couplings align with four-dimensional N=2 supergravity, with Hitchin functionals playing a key role.

Contribution

It demonstrates that the moduli space of such backgrounds has a special Kähler geometry characterized by Hitchin functionals and derives the N=2 superpotential explicitly.

Findings

Moduli space admits a special Kähler geometry with Hitchin functionals.

Couplings match those of four-dimensional N=2 supergravity after reduction.

Explicit form of the N=2 superpotential derived from gravitino transformations.

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.