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(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.

IIB black hole horizons with five-form flux and extended supersymmetry

“…This is in analogy with similar results that have been obtained for the horizons of heterotic supergravity [7,8]. However unlike for heterotic supergravity [11][12][13], there is no complete classification of solutions to the KSEs of IIB supergravity. The solution of the KSEs of IIB supergravity is known only for backgrounds preserving one supersymmetry [14,15] and for backgrounds with nearly maximal number of supersymmetries [16][17][18][19].…”

Anomaly corrected heterotic horizons

“…Firstly, from the perspective of the standard supergravity, much more is known about the geometric structure of generic supersymmetric solutions, and near-horizon geometries. In particular, as a consequence of the spinorial geometry classification techniques developed in [25,26] which were then combined with a global analysis of near-horizon geometries in [27], there exists a full classification of all possible supersymmetric near-horizon geometries in the heterotic supergravity. Secondly, the structure of higher derivative correction terms in the field equations, and in the Killing spinor equations, is significantly simpler for the heterotic theory when compared to the types of terms which arise in type II supergravity [29][30][31][32], and associated references.…”

Geometry and supersymmetry of heterotic warped flux AdS backgrounds

“…In particular, the equations (3.15), (3.16), (3.17) and (3.18) are still valid but now exactly. The only modification is in the second equation in (3.17) which now reads 26) whereR (6) is a su(3) instanton on B 6 , ieR (6) is a (1,1)-form and ω-traceless. This condition is also satisfied by F because of the gaugino KSE.…”