Systematics of M-theory spinorial geometry

Abstract

We reduce the classification of all supersymmetric backgrounds in eleven dimensions to the evaluation of the supercovariant derivative and of an integrability condition, which contains the field equations, on six types of spinors. We determine the expression of the supercovariant derivative on all six types of spinors and give in each case the field equations that do not arise as the integrability conditions of Killing spinor equations. The Killing spinor equations of a background become a linear system for the fluxes, geometry and spacetime derivatives of the functions that determine the spinors. The solution of the linear system expresses the fluxes in terms of the geometry and specifies the restrictions on the geometry of spacetime for all supersymmetric backgrounds. We also show that the minimum number of field equations that is needed for a supersymmetric configuration to be a solution of eleven-dimensional supergravity can be found by solving a linear system. The linear systems of the Killing spinor equations and their integrability conditions are given in both a timelike and a null spinor basis. We illustrate the construction with examples.

46 pages. v2: systematics of a null spinor basis is included in section 5

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Cited by in corpus (44)

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• Characterization of all the supersymmetric solutions of gauged N=1,d=5 supergravity
• General Supersymmetric Solutions of Five-Dimensional Supergravity
• All the supersymmetric solutions of N=1,d=5 ungauged supergravity
• Systematics of IIB spinorial geometry
• N=31, D=11
• All the supersymmetric configurations of N=4,d=4 supergravity
• All null supersymmetric backgrounds of N=2, D=4 gauged supergravity coupled to abelian vector multiplets
• Geometry of four-dimensional Killing spinors
• Supersymmetry of AdS and flat backgrounds in M-theory
• Classification, geometry and applications of supersymmetric backgrounds
• Supersymmetric wrapped membranes, AdS(2) spaces, and bubbling geometries
• Supersymmetric solutions of gauged five-dimensional supergravity with general matter couplings
• All the timelike supersymmetric solutions of all ungauged d=4 supergravities
• Index theory and dynamical symmetry enhancement of M-horizons
• The supersymmetric solutions and extensions of ungauged matter-coupled N=1,d=4 supergravity
• M-theory backgrounds with 30 Killing spinors are maximally supersymmetric
• The geometry of extended null supersymmetry in M-theory
• Eight-manifolds with G-structure in eleven dimensional supergravity
• Non-Abelian T-duality for nonrelativistic holographic duals
• Static M-horizons
• M-Horizons
• Geometry of type II common sector N=2 backgrounds
• Aspects of spinorial geometry
• Invariant Killing spinors in 11D and type II supergravities
• Supersymmetric geometries of IIA supergravity III
• Real Killing Spinors in Neutral Signature
• Supersymmetric geometries of IIA supergravity II
• Spinorial Geometry and Supergravity
• Spinning strings in AdS_5 x S^5: A worldsheet perspective
• Kappa symmetry, generalized calibrations and spinorial geometry
• Supersymmetric $d{S}_n$ solutions for $n\ge 5$ in $D=11$ supergravity
• Decomposable $(4,7)$ solutions in eleven-dimensional supergravity
• Supersymmetric dS4 solutions in D=11 supergravity
• N=4 Near-Horizon Geometries in D=11 Supergravity
• Dynamical supersymmetry enhancement of black hole horizons
• Non-compact manifolds with Killing spinors
• Neutral Signature Gauged Supergravity Solutions
• $D=11$ $d{S}_5$ backgrounds with enhanced supersymmetry
• Spinorial geometry, horizons and superconformal symmetry in six dimensions
• Killing Spinors -- Beyond Supergravity