The Geometry of D=11 Killing Spinors

TL;DR

This paper classifies all supersymmetric solutions of D=11 supergravity using G-structures derived from Killing spinors, identifying geometric structures and conditions for solutions, including new rotating and Godel solutions.

Contribution

It introduces a classification scheme for D=11 supergravity solutions based on G-structures from Killing spinors, detailing geometric conditions and presenting new solutions.

Findings

Most geometries admit SU(5) or Spin(7) structures depending on the Killing vector

The geometry is largely determined by the identified G-structure

New solutions include rotating resolved membranes and Godel universes

Abstract

We propose a way to classify all supersymmetric configurations of D=11 supergravity using the G-structures defined by the Killing spinors. We show that the most general bosonic geometries admitting a Killing spinor have at least a local SU(5) or an (Spin(7)\ltimes R^8)x R structure, depending on whether the Killing vector constructed from the Killing spinor is timelike or null, respectively. In the former case we determine what kind of local SU(5) structure is present and show that almost all of the form of the geometry is determined by the structure. We also deduce what further conditions must be imposed in order that the equations of motion are satisfied. We illustrate the formalism with some known solutions and also present some new solutions including a rotating generalisation of the resolved membrane solutions and generalisations of the recently constructed D=11 Godel solution.