Supersymmetric geometries of IIA supergravity III

TL;DR

This paper classifies supersymmetric (massive) IIA supergravity backgrounds with a specific G2-invariant Killing spinor, revealing geometric structures like null Killing vectors and G2 instanton conditions, and expresses fluxes in geometric terms.

Contribution

It completes the classification of all (massive) IIA backgrounds preserving one supersymmetry with G2-invariant Killing spinors, extending previous results and analyzing special geometric cases.

Findings

Existence of a null Killing vector leaving the spinor invariant.

Rotation of the Killing vector satisfies a G2 instanton condition.

Fluxes are expressed in terms of geometric data.

Abstract

We find that (massive) IIA backgrounds that admit a $G_2\ltimes \mathbb{R}^8$ invariant Killing spinor must exhibit a null Killing vector field which leaves the Killing spinor invariant and that the rotation of the Killing vector field satisfies a certain $\mathfrak{g}_2$ instanton condition. This result together with those in [4] and [5] complete the classification of geometries of all (massive) IIA backgrounds that preserve one supersymmetry. We also explore the geometry of a class of backgrounds which admit a $G_2\ltimes \mathbb{R}^8$ invariant Killing spinor and where in addition an appropriate 1-form bilinear vanishes. In all cases, we express the fluxes of the theory in terms of the geometry.