Supersymmetry and homogeneity of M-theory backgrounds

TL;DR

This paper constructs a Lie superalgebra for supersymmetric M-theory backgrounds and proves that backgrounds with more than 24 supercharges are necessarily locally homogeneous.

Contribution

It introduces a Lie superalgebra framework for M-theory backgrounds and establishes a threshold for homogeneity based on the number of supercharges.

Findings

Backgrounds with >24 supercharges are locally homogeneous.

Constructs a Lie superalgebra associated with supersymmetric backgrounds.

Proves local transitivity of the bosonic subalgebra in high-supersymmetry backgrounds.

Abstract

We describe the construction of a Lie superalgebra associated to an arbitrary supersymmetric M-theory background, and discuss some examples. We prove that for backgrounds with more than 24 supercharges, the bosonic subalgebra acts locally transitively. In particular, we prove that backgrounds with more than 24 supersymmetries are necessarily (locally) homogeneous.