The Killing superalgebra of ten-dimensional supergravity backgrounds

Abstract

We construct the Killing superalgebra of supersymmetric backgrounds of ten-dimensional heterotic and type II supergravities and prove that it is a Lie superalgebra. We also show that if the fraction of supersymmetry preserved by the background is greater than 1/2, in the heterotic case, or greater than 3/4 in the type II case, then the background is locally homogeneous.

21 pages; V2: 3 references added; V3: 1 reference added and two imprecisions corrected; V4: small changes due to error in a separate paper

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• A note on supersymmetric AdS_6 solutions of massive type IIA supergravity
• D-branes on AdS flux compactifications
• Generalized structures of ten-dimensional supersymmetric solutions
• The homogeneity theorem for supergravity backgrounds
• Classification, geometry and applications of supersymmetric backgrounds
• Supersymmetric Backgrounds, the Killing Superalgebra, and Generalised Special Holonomy
• IIB solutions with N>28 Killing spinors are maximally supersymmetric
• Index theory and dynamical symmetry enhancement near IIB horizons
• Killing superalgebras for Lorentzian four-manifolds
• All Killing Superalgebras for Warped AdS Backgrounds
• Symmetric backgrounds of type IIB supergravity
• Conformal symmetry superalgebras
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• The Cauchy problem for parallel spinors as first-order symmetric hyperbolic system
• Hidden symmetries and Lie algebra structures from geometric and supergravity Killing spinors
• Supersymmetric geometries of IIA supergravity III
• Symmetric M-Theory Backgrounds
• Generalized symmetry superalgebras
• Extended superalgebras from twistor and Killing spinors
• Supersymmetric geometries of IIA supergravity II
• Higher-dimensional field theories from type II supergravity
• Superspaces for heterotic pure spinor string compactifications
• Conformal superalgebras via tractor calculus
• All superalgebras for warped AdS${}_2$ and black hole near horizon geometries
• Deformations of M-theory Killing superalgebras
• Killing superalgebra deformations of ten-dimensional supergravity backgrounds
• Half-BPS M2-brane orbifolds
• The Classification of Highly Supersymmetric Supergravity Solutions
• Knots in $SU\left(M|N\right)$ Chern-Simons Field Theory
• Einstein-Yang-Mills fields immune to quantum corrections
• Submaximal conformal symmetry superalgebras for Lorentzian manifolds of low dimension
• Rigidity of Killing-Yano and conformal Killing-Yano superalgebras