Remarks on highly supersymmetric backgrounds of 11-dimensional supergravity

TL;DR

This paper explores the mathematical structure of highly supersymmetric backgrounds in 11-dimensional supergravity, establishing a correspondence with abstract symbols and providing methods to construct and analyze such backgrounds.

Contribution

It introduces the concept of abstract symbols, proves a strong Reconstruction Theorem, and offers a strategy and example for constructing highly supersymmetric supergravity backgrounds.

Findings

Established a bijective correspondence between backgrounds and abstract symbols.

Computed the ideal generated by Killing spinors in specific pp-wave backgrounds.

Provided an alternative proof of a supersymmetry gap result.

Abstract

This note focuses on some properties and uses of filtered deformations in the context of D=11 supergravity. We define the concept of abstract symbol and give a strong version of the Reconstruction Theorem, namely a bijective correspondence from the space of highly supersymmetric supergravity backgrounds to the space of abstract symbols. We propose a general strategy to construct highly supersymmetric supergravity backgrounds and present an example in detail, which includes the computation of the ideal generated by the Killing spinors of two known pp-wave backgrounds with N=24 supersymmetry. Finally, we give an alternative proof, based on the isotropy algebra of a supergravity background, of a classical supersymmetry gap result of Gran, Gutowski, Papadopoulos and Roest.