Geometry of all supersymmetric type I backgrounds

Abstract

We find the geometry of all supersymmetric type I backgrounds by solving the gravitino and dilatino Killing spinor equations, using the spinorial geometry technique, in all cases. The solutions of the gravitino Killing spinor equation are characterized by their isotropy group in Spin(9,1), while the solutions of the dilatino Killing spinor equation are characterized by their isotropy group in the subgroup Sigma(P) of Spin(9,1) which preserves the space of parallel spinors P. Given a solution of the gravitino Killing spinor equation with L parallel spinors, L = 1,2,3,4,5,6,8, the dilatino Killing spinor equation allows for solutions with N supersymmetries for any 0 < N =< L. Moreover for L = 16, we confirm that N = 8,10,12,14,16. We find that in most cases the Bianchi identities and the field equations of type I backgrounds imply a further reduction of the holonomy of the supercovariant connection. In addition, we show that in some cases if the holonomy group of the supercovariant connection is precisely the isotropy group of the parallel spinors, then all parallel spinors are Killing and so there are no backgrounds with N < L supersymmetries.

73 pages. v2: minor changes, references added

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• Supergravity vacua and lorentzian Lie groups
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• Gauduchon-Tod structures, Sim holonomy and De Sitter supergravity
• HKT Geometry and de Sitter Supergravity
• New half supersymmetric solutions of the heterotic string
• Supersymmetric solutions of gauged five-dimensional supergravity with general matter couplings
• Compact supersymmetric solutions of the heterotic equations of motion in dimension 5
• IIB backgrounds with five-form flux
• Invariant Killing spinors in 11D and type II supergravities
• Solution of heterotic Killing spinor equations and special geometry
• The Classification of Highly Supersymmetric Supergravity Solutions