Geometry of all supersymmetric type I backgrounds
نویسندگان
چکیده
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 Σ(P) of Spin(9, 1) which preserves the space of parallel spinors P. 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.
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