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 Σ(Script P) of Spin(9, 1) which preserves the space of parallel spinors Script 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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 August 2007
 DOI:
 10.1088/11266708/2007/08/074
 arXiv:
 arXiv:hepth/0703143
 Bibcode:
 2007JHEP...08..074G
 Keywords:

 High Energy Physics  Theory
 EPrint:
 73 pages. v2: minor changes, references added