The cohomological structure of generalized Killing spinor equations

TL;DR

This paper reviews a topological framework within supergravity theories that enables a cohomological reformulation of generalized Killing spinor equations, aiding in understanding supersymmetric solutions.

Contribution

It introduces a cohomological reformulation of Killing spinor equations based on a recently discovered topological structure in supergravity.

Findings

Cohomological reformulation simplifies analyzing supersymmetric solutions.

Topological structure applies across various supergravity theories.

Provides new tools for classifying unbroken supersymmetry solutions.

Abstract

We review the topological structure, sitting in any supergravity theory, which has been recently discovered in arXiv: 1801.04940. We describe how such a structure allows for a cohomological reformulation of the generalized Killing spinor equations which characterize bosonic supergravity solutions with unbroken supersymmetry.