M-theory backgrounds with 30 Killing spinors are maximally supersymmetric

TL;DR

This paper proves that in M-theory, backgrounds with more than 29 Killing spinors must be maximally supersymmetric, showing no intermediate solutions exist with exactly 30 supersymmetries.

Contribution

It establishes a rigidity result for M-theory backgrounds, demonstrating that 30 supersymmetries imply maximal supersymmetry, with no exceptions or quotients.

Findings

All backgrounds with >29 Killing spinors are maximally supersymmetric.

Supercovariant curvature vanishes for backgrounds with 30 supersymmetries.

No solutions with 30 supersymmetries are discrete quotients of maximally supersymmetric backgrounds.

Abstract

We show that all M-theory backgrounds which admit more than 29 Killing spinors are maximally supersymmetric. In particular, we find that the supercovariant curvature of all backgrounds which preserve 30 supersymmetries, subject to field equations and Bianchi identities, vanishes, and that there are no such solutions which arise as discrete quotients of maximally supersymmetric backgrounds.