Reducing democratic type II supergravity on SU(3) x SU(3) structures

TL;DR

This work derives the full bosonic action for four-dimensional N=2 gauged supergravity arising from type II compactifications on manifolds with SU(3)×SU(3) structure, using the democratic RR formulation and generalized geometry. It provides a geometric expression for the complete N=2 scalar potential and implements a finite-mode truncation, yielding a symplectically invariant NSNS+RR action with tensor multiplets and a consistent set of 4d EoMs and Bianchi identities. The RR sector is reduced via its equations of motion and self-duality constraints, reproducing the D’Auria–FerrTrigiante framework for electric/magnetic gaugings and tensor couplings, and matching known special-Kähler and quaternionic structures. The results generalize Calabi–Yau reductions to broader internal geometries, offer a unifying 4d viewpoint for flux compactifications, and pave the way for controlled N=1 truncations and explicit model-building within generalized geometry.

Abstract

Type II supergravity on backgrounds admitting SU(3) x SU(3) structure and general fluxes is considered. Using the generalized geometry formalism, we study dimensional reductions leading to N=2 gauged supergravity in four dimensions, possibly with tensor multiplets. In particular, a geometric formula for the full N=2 scalar potential is given. Then we implement a truncation ansatz, and derive the complete N=2 bosonic action. While the NSNS contribution is obtained via a direct dimensional reduction, the contribution of the RR sector is computed starting from the democratic formulation and demanding consistency with the reduced equations of motion.