Aspects of spinorial geometry

TL;DR

This paper reviews the spinorial geometry method for classifying supersymmetric solutions in supergravity, detailing how it simplifies Killing spinor equations and applying it to classify maximally supersymmetric backgrounds.

Contribution

It introduces a linear system approach to express fluxes and geometry, and applies this to classify specific supersymmetric backgrounds in supergravity theories.

Findings

Classified maximally supersymmetric G-backgrounds in IIB supergravity.

Derived the most general pp-wave solutions preserving half supersymmetry.

Classified N=31 backgrounds in ten and eleven dimensions.

Abstract

We review some aspects of the spinorial geometry approach to the classification of supersymmetric solutions of supergravity theories. In particular, we explain how spinorial geometry can be used to express the Killing spinor equations in terms of a linear system for the fluxes and the geometry of spacetime. The solutions of this linear system express some of the fluxes in terms of the spacetime geometry and determine the conditions on the spacetime geometry imposed by supersymmetry. We also present some of the recent applications like the classification of maximally supersymmetric G-backgrounds in IIB, this includes the most general pp-wave solution preserving 1/2 supersymmetry, and the classification of N=31 backgrounds in ten and eleven dimensions.