N=1,2 supersymmetric vacua of IIA supergravity and SU(2) structures

TL;DR

This work analyzes $ ext{N}=1$ and $ ext{N}=2$ supersymmetric warped compactifications of massive IIA supergravity on $M_{1,3} imes_req X_6$ with $X_6$ carrying an $SU(2)$ structure. By reformulating the Killing-spinor equations in terms of $SU(2)$-structure data, the authors derive internal constraints and perform a truncation to compare with Minkowski and AdS$_4$ backgrounds. Under a consistent truncation retaining only scalar fluxes and a constant dilaton, they prove no $ ext{N}=1$ vacua with nonzero Romans mass exist, and further show no $ ext{N}=2$ AdS$_4$ vacua arise for their chosen Ansätze. They discuss the necessity of extra ingredients (sources, noncompact spaces, or higher-order corrections) to evade the no-go results, highlighting how $SU(2)$-structure imposes strong restrictions on flux configurations. The results map the limitations of simple flux vacua in massive IIA on $SU(2)$-structured manifolds and inform directions for finding more general solutions.

Abstract

We consider backgrounds of (massive) IIA supergravity of the form of a warped product $M_{1,3}\times_ω X_6$, where $X_6$ is a six-dimensional compact manifold and $M_{1,3}$ is $AdS_4$ or a four-dimensional Minkowski space. We analyse conditions for $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry on manifolds of SU(2) structure. We prove the absence of solutions in certain cases.