Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-03-04
Class.Quant.Grav.22:2701-2744,2005
Physics
High Energy Physics
High Energy Physics - Theory
46 pages. v2: systematics of a null spinor basis is included in section 5
Scientific paper
10.1088/0264-9381/22/13/013
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.
Gran Ulf
Papadopoulos George
Roest Diederik
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