Hitchin Functionals in N=2 Supergravity

TL;DR

The paper demonstrates that type II string theory backgrounds with SU(3)×SU(3) structure can be reformulated in a four-dimensional N=2–like framework using generalized geometry, where Hitchin functionals provide the Kahler potentials for the NS moduli. By rewriting the ten-dimensional theory in Spin(1,3)×O(6,6) language and performing a careful finite truncation, the authors derive two decoupled special Kahler moduli spaces and read off the N=2 Killing prepotentials from gravitino transformations, identifying their dependence on fluxes and intrinsic torsion. The work further constructs the general N=1 superpotential via an N=2 to N=1 truncation, recovers known GVW-like expressions in appropriate limits, and shows how the four-dimensional theory becomes gauged supergravity with gaugings tied to fluxes and torsion. Finally, the paper discusses mirror symmetry in this generalized context and outlines how a complete SU(3)×SU(3) formulation may restore a fuller mirror map, pointing to broader implications for topological string connections and extended backgrounds.

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.