The Killing superalgebra of ten-dimensional supergravity backgrounds

TL;DR

This paper constructs the Killing superalgebra for ten-dimensional supergravity backgrounds, proving it forms a Lie superalgebra and establishing conditions for local homogeneity based on supersymmetry fraction.

Contribution

It provides a rigorous construction of the Killing superalgebra in ten-dimensional supergravity and links supersymmetry preservation to local homogeneity of backgrounds.

Findings

Killing superalgebra is a Lie superalgebra.

Backgrounds with >1/2 supersymmetry in heterotic case are locally homogeneous.

Backgrounds with >3/4 supersymmetry in type II case are locally homogeneous.

Abstract

We construct the Killing superalgebra of supersymmetric backgrounds of ten-dimensional heterotic and type II supergravities and prove that it is a Lie superalgebra. We also show that if the fraction of supersymmetry preserved by the background is greater than 1/2, in the heterotic case, or greater than 3/4 in the type II case, then the background is locally homogeneous.