Null structure groups in eleven dimensions

Abstract

We classify all the structure groups which arise as subgroups of the isotropy group, $(Spin(7)⋉{\mathbb{R}}^8)\times \mathbb{R}$, of a single null Killing spinor in eleven dimensions. We construct the spaces of spinors fixed by these groups. We determine the conditions under which structure subgroups of the maximal null strucuture group $(Spin(7)⋉{\mathbb{R}}^8)\times \mathbb{R}$ may also be embedded in SU(5), and hence the conditions under which a supersymmetric spacetime admits only null, or both timelike and null, Killing spinors. We discuss how this purely algebraic material will facilitate the direct analysis of the Killing spinor equation of eleven dimensional supergravity, and the classification of supersymmetric spacetimes therein.

25 pages, Latex. v2: substantially modified discussion of results. Generic N=2 structure group with one null Killing spinor is SU(2), not the identity. v3:typos corrected. v4: minor modifications in response to referee's comments, typos corrected. Final version to appear in Phys.Rev.D

References in corpus (32)

• All supersymmetric solutions of minimal supergravity in five dimensions
• A supersymmetric black ring
• Superstrings with Intrinsic Torsion
• The Geometry of D=11 Killing Spinors
• G-Structures and Wrapped NS5-Branes
• Supersymmetric Backgrounds from Generalized Calabi-Yau Manifolds
• Supersymmetric AdS_5 solutions of M-theory
• All supersymmetric solutions of minimal supergravity in six dimensions
• All supersymmetric solutions of minimal gauged supergravity in five dimensions
• G-Structures, Fluxes and Calibrations in M-Theory
• The Geometry of D=11 Null Killing Spinors
• The spinorial geometry of supersymmetric backgrounds
• The general form of supersymmetric solutions of N=(1,0) U(1) and SU(2) gauged supergravities in six dimensions
• Supersymmetry and homogeneity of M-theory backgrounds
• On supersymmetric solutions of type IIB supergravity with general fluxes
• One Ring to Rule Them All ... and in the Darkness Bind Them?
• Type IIB Killing spinors and calibrations
• More on BPS solutions of N=2, D=4 gauged supergravity
• Notes on SU(3) Structures in Type IIB Supergravity
• M-theory compactification, fluxes and AdS_4
• Refining G-structure classifications
• Generalizing the N=2 supersymmetric RG flow solution of IIB supergravity
• Bubbling AdS3
• Timelike Killing spinors in seven dimensions
• Generalized holonomy of M-theory vacua
• Classification of supersymmetric spacetimes in eleven dimensions
• Eight-manifolds with G-structure in eleven dimensional supergravity
• The geometry of extended null supersymmetry in M-theory
• N=1 supersymmetric solutions of IIB supergravity
• A Family of M-theory Flows with Four Supersymmetries
• Fluxes in M-theory on 7-manifolds: G_2-, SU(3)- and SU(2)-structures
• Type IIA Killing spinors and calibrations

Cited by in corpus (18)

• The supersymmetric configurations of N=2, d=4 supergravity coupled to vector supermultiplets
• AdS spacetimes from wrapped M5 branes
• Characterization of all the supersymmetric solutions of gauged N=1,d=5 supergravity
• All the supersymmetric solutions of N=1,d=5 ungauged supergravity
• New supersymmetric AdS_3 solutions
• All the supersymmetric configurations of N=4,d=4 supergravity
• Supersymmetric AdS3 X S2 M-theory geometries with fluxes
• Global geometry of the supersymmetric AdS_3/CFT_2 correspondence in M-theory
• Supersymmetric wrapped membranes, AdS(2) spaces, and bubbling geometries
• AdS spacetimes from wrapped D3-branes
• Supersymmetric solutions of gauged five-dimensional supergravity with general matter couplings
• The supersymmetric solutions and extensions of ungauged matter-coupled N=1,d=4 supergravity
• Classification of supersymmetric spacetimes in eleven dimensions
• The geometry of extended null supersymmetry in M-theory
• Eight-manifolds with G-structure in eleven dimensional supergravity
• Invariant Killing spinors in 11D and type II supergravities
• Spinorial Geometry and Supergravity
• Central charges of wrapped M5-brane backgrounds