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

TL;DR

This paper investigates supersymmetric vacua in massive IIA supergravity with warped product geometries, analyzing conditions for N=1 and N=2 supersymmetry on SU(2) structured manifolds, and proving the absence of solutions in some cases.

Contribution

It provides a detailed analysis of supersymmetric solutions in IIA supergravity with SU(2) structures, including new no-go theorems for certain configurations.

Findings

No solutions for specific SU(2) structures under certain conditions.

Conditions for N=1 and N=2 supersymmetry on warped products.

Characterization of supersymmetric vacua in IIA supergravity.

Abstract

We consider backgrounds of (massive) IIA supergravity of the form of a warped product $M_{1,3}\times_{\omega} X_6$, 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.