Nearly Kaehler Reduction

TL;DR

This work constructs the first explicit reduction of type IIA supergravity on nearly Kahler manifolds, leveraging the Laplacian-eigenform property of $J$ and $\Omega$ to define a minimal expansion ansatz. The resulting 4d theory is ${\cal N}=2$ gauged supergravity with a single vector multiplet and the universal hypermultiplet, incorporating both electric and magnetic gaugings via tensor multiplets; fluxes $F_0, F_2, F_4, F_6$ (or $G_0, G_6$) are related to the 4d moduli and ultimately match known 10d backgrounds. The authors demonstrate that supersymmetric 4d configurations lift to 10d nearly Kahler backgrounds in agreement with prior Behrndt–Lust–Grana analyses, providing explicit flux expressions and a concrete realization of the symplectic gauging framework. They also discuss the limitations of the truncation in capturing all light modes and emphasize the role of a one-parameter family of nearly Kahler structures in the reduction. Overall, the paper strengthens the link between 4d ${\cal N}=2$ gauged supergravity and 10d flux compactifications on SU(3) structure manifolds, via a controlled and intrinsic reduction.

Abstract

We consider compactification of type IIA supergravity on nearly Kaehler manifolds. These represent a simple class of SU(3) structure manifolds which includes S^6 and CP^3. We exhibit for the first time an explicit reduction ansatz in this context, obtaining an N=2 gauged supergravity in 4d with a single vector and hypermultiplet. We verify that supersymmetric solutions of the 4d theory lift to 10d solutions. Along the way, we discuss questions related to encountering both electric and magnetic charges in the 4d theory.