A note on a relation between the Killing spinor and Einstein equations

TL;DR

This paper demonstrates that the presence of a Killing spinor under specific conditions guarantees the Einstein equations are satisfied, leading to a new supersymmetric black fivebrane solution in D=11 supergravity.

Contribution

It establishes a link between Killing spinors and Einstein equations, and constructs a novel black fivebrane solution with K3×R topology.

Findings

Existence of Killing spinor implies Einstein equations under certain conditions.

Derived a new supersymmetric black fivebrane solution in D=11 supergravity.

The solution preserves 1/4 of the supersymmetries.

Abstract

It is shown that, under certain conditions, the existence of a Killing spinor on a bosonic background of a supergravity theory implies that the Einstein equations are also satisfied. As an application of the theorem, we obtain a new black fivebrane solution of D=11 supergravity, which has $K3\times R$ topology and preserves 1/4'th supersymmetries of the theory.