IIA supergravity and M-theory on manifolds with SU(4) structure

TL;DR

The paper develops a comprehensive framework for supersymmetric backgrounds in M-theory and massive IIA on eight-manifolds with $SU(4)$ structure that preserve two real supercharges. It derives the general IIA solution with a strict $SU(4)$ ansatz, analyzes integrability in low dimensions, and specializes to Calabi–Yau fourfolds, revealing that SUSY can persist with non-(2,2) or non-primitive fluxes; it provides an uplift to M-theory, formulates 3D superpotential descriptions, and constructs explicit flux vacua on $K3 imes K3$ with varying amounts of preserved supersymmetry. The work connects these backgrounds to three-dimensional gauged supergravity, clarifies no-go and correction mechanisms, and points toward higher-dimensional analogues of Klebanov-Strassler geometries and potential F-theory duals. Overall, it broadens the landscape of controlled flux vacua in lower dimensions and supplies concrete, calculable examples for further holographic and phenomenological exploration.

Abstract

We give the general form of supersymmetric backgrounds with two real supercharges of M-theory and type IIA supergravity (with non-zero Romans mass in general) of the form $\mathbb{R}^{1,d} \times \M_8$, d=1,2, on eight-dimensional manifolds with SU(4) structure. We point out a subtlety in the integrability theorems for low-dimensional supersymmetric compactifications. As a special case we examine Calabi-Yau flux vacua and we show that unbroken supersymmetry does not in general require the four-form flux to be (2,2) or primitive. Our results could be used to construct novel higher-dimensional analogues of the Klebanov-Strassler geometry. In the case of M-theory large-volume Calabi-Yau flux vacua our results are in agreement with partial supersymmetry breaking in three-dimensional N=2 supergravity. Alternatively, the conditions for supersymmetry can be expressed in terms of a real `superpotential' in accordance with three-dimensional N=1 supergravity. We present explicit examples of M-theory flux vacua on K3 \times K3, which however do not appear to possess F-theory duals with four-dimensional Poincaré invariance.