The homogeneity theorem for supergravity backgrounds

TL;DR

This paper proves that supergravity backgrounds preserving more than half of the supersymmetry are necessarily locally homogeneous, with homogeneity directly arising from the supersymmetry itself, in 10- and 11-dimensional theories.

Contribution

It establishes the strong homogeneity conjecture for supergravity backgrounds, linking high supersymmetry preservation to local homogeneity in 10- and 11-dimensional theories.

Findings

Supergravity backgrounds with >50% supersymmetry are locally homogeneous.

Homogeneity is generated by Killing vectors from Killing spinors.

The proof applies to eleven-dimensional and type I/heterotic/type II supergravity theories.

Abstract

We prove the strong homogeneity conjecture for eleven- and ten-dimensional (Poincar\'e) supergravity backgrounds. In other words, we show that any backgrounds of 11-dimensional, type I/heterotic or type II supergravity theories preserving a fraction greater than one half of the supersymmetry of the underlying theory are necessarily locally homogeneous. Moreover we show that the homogeneity is due precisely to the supersymmetry, so that at every point of the spacetime one can find a frame for the tangent space made out of Killing vectors constructed out of the Killing spinors.