The spinorial geometry of supersymmetric heterotic string backgrounds
Abstract
We determine the geometry of supersymmetric heterotic string backgrounds for which all parallel spinors with respect to the connection hat nabla with torsion H, the NSotimesNS threeform field strength, are Killing. We find that there are two classes of such backgrounds, the null and the timelike. The Killing spinors of the null backgrounds have stability subgroups KltimesBbb R^{8} in Spin(9,1), for K = Spin(7), SU(4), Sp(2), SU(2)×SU(2) and {1}, and the Killing spinors of the timelike backgrounds have stability subgroups G_{2}, SU(3), SU(2) and {1}. The former admit a single null hat nablaparallel vector field while the latter admit a timelike and two, three, five and nine spacelike hat nablaparallel vector fields, respectively. The spacetime of the null backgrounds is a Lorentzian twoparameter family of Riemannian manifolds B with skewsymmetric torsion. If the rotation of the null vector field vanishes, the holonomy of the connection with torsion of B is contained in K. The spacetime of timelike backgrounds is a principal bundle P with fibre a Lorentzian Lie group and base space a suitable Riemannian manifold with skewsymmetric torsion. The principal bundle is equipped with a connection λ which determines the nonhorizontal part of the spacetime metric and of H. The curvature of λ takes values in an appropriate Lie algebra constructed from that of K. In addition dH has only horizontal components and contains the Pontrjagin class of P. We have computed in all cases the Killing spinor bilinears, expressed the fluxes in terms of the geometry and determine the field equations that are implied by the Killing spinor equations.
 Publication:

Journal of High Energy Physics
 Pub Date:
 February 2006
 DOI:
 10.1088/11266708/2006/02/063
 arXiv:
 arXiv:hepth/0510176
 Bibcode:
 2006JHEP...02..063G
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Differential Geometry
 EPrint:
 73pp. v2: minor changes