Supersymmetric AdS(4) compactifications of IIA supergravity

TL;DR

This work identifies necessary and sufficient conditions for ${ m N}=1$ AdS$_4$ compactifications of massive IIA via $SU(3)$ structures, revealing a new class of solutions with constant dilaton and fluxes for all form fields on a half-flat internal manifold $X_6$. The internal torsion is constrained to ${f W}^-_1
3bf W}^-_2$, with ${ m d}{f W}_2^-\u221d { m Re}(oldsymbol extOmega)$, and all flux components are fixed by geometry; the results include a massless limit that lifts to M-theory as a twisted circle over $X_6$. Explicit constructions such as $T^2$ fibrations over K3 and the Iwasawa manifold illustrate the geometry but also show that not all half-flat examples satisfy the precise Bianchi constraints required for the AdS$_4$ vacua. Overall, the paper advances the classification of flux vacua in massive IIA and clarifies the role of half-flat $SU(3)$-structure manifolds in achieving consistent AdS$_4$ backgrounds.

Abstract

We derive necessary and sufficient conditions for N=1 compactifications of (massive) IIA supergravity to AdS(4) in the language of SU(3) structures. We find new solutions characterized by constant dilaton and nonzero fluxes for all form fields. All fluxes are given in terms of the geometrical data of the internal compact space. The latter is constrained to belong to a special class of half-flat manifolds.