Type-IIA flux compactifications and N=4 gauged supergravities

TL;DR

This work establishes a precise map between Type-IIA flux compactifications preserving (exact or spontaneously broken) N=4 supersymmetry in four dimensions and gauged N=4 supergravity, linking ten-dimensional flux/Bianchi identities to four-dimensional generalized structure constants and Jacobi constraints. It provides an explicit dictionary including de Roo–Wagemans phases, identifies the electric/magnetic vector content, and derives the resulting gauging from RR/NSNS fluxes, showing consistency with Bianchi identities and illuminating when ξ terms can arise. The authors apply this framework to construct an AdS4 family with spontaneous breaking from N=4 to N=1, embedded in an N=8 context, and analyze the geometry of the corresponding massive IIA vacuum, which is described by a nearly-Kähler Y6 with two RR fluxes and exhibits a Scherk–Schwarz reduction to SU(2). These results advance understanding of moduli stabilization, gauge algebras in flux compactifications, and the holographic duals of extended-supersymmetry flux vacua.

Abstract

We establish the precise correspondence between Type-IIA flux compactifications preserving an exact or spontaneously broken N=4 supersymmetry in four dimensions, and gaugings of their effective N=4 supergravities. We exhibit the explicit map between fluxes and Bianchi identities in the higher-dimensional theory and generalized structure constants and Jacobi identities in the reduced theory, also detailing the origin of gauge groups embedded at angles in the duality group. We present AdS4 solutions of the massive Type-IIA theory with spontaneous breaking to N=1, at small string coupling and large volume, and discuss their dual CFT3.