Supersymmetric geometries of IIA supergravity II

TL;DR

This paper classifies supersymmetric solutions in IIA supergravity with SU(4) symmetry, revealing geometric constraints including a time-like Killing vector that preserves the fields and spinor.

Contribution

It provides a detailed solution to the Killing spinor equations for specific SU(4) invariant spinors in IIA supergravity, elucidating the associated spacetime geometry.

Findings

Existence of a time-like Killing vector field.

Constraints on spacetime geometry from Killing spinor equations.

Identification of supersymmetric geometries with SU(4) symmetry.

Abstract

We solve the Killing spinor equations of standard and massive IIA supergravities for a Killing spinor whose isotropy subgroup in Spin(9, 1) is SU(4) and identify the geometry of the spacetime. We demonstrate that the Killing spinor equations impose some mild constraints on the geometry of the spacetime which include the existence of a time-like Killing vector field which leaves the fields and the Killing spinor invariant.