2005/10/31 by Ulf Gran, U. Gran, Philipp Lohrmann +2 · 5 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Connection (principal bundle) #Curvature #Gauge theory #Geometry #Geometry and complex manifolds #Heterotic string theory #Holonomy #Killing spinor #Killing vector field #Mathematical physics #Mathematics #Minkowski space #Nabla symbol #Nonlinear Waves and Solitons #Physics #Quantum mechanics #Riemann curvature tensor #Spacetime #Spin connection #Spinor #Supergravity #Supersymmetry #Torsion (gastropod) #hep-th #math.DG
paper · pdf · doi:10.1088/1126-6708/2006/02/063
published as JHEP 0602:063,2006 · 73pp. v2: minor changes
arxiv created 2005/12/20 · openalex publication_date 2006/02/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We determine the geometry of supersymmetric heterotic string backgrounds for which all parallel spinors with respect to the connection ∇ with torsion H, the NS⊗NS three-form 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 K\ltimes\bR8 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 G2, SU(3), SU(2) and \1\. The former admit a single null ∇-parallel vector field while the latter admit a timelike and two, three, five and nine spacelike ∇-parallel vector fields, respectively. The spacetime of the null backgrounds is a Lorentzian two-parameter family of Riemannian manifolds B with skew-symmetric 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 time-like backgrounds is a principal bundle P with fibre a Lorentzian Lie group and base space a suitable Riemannian manifold with skew-symmetric torsion. The principal bundle is equipped with a connection λ which determines the non-horizontal 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.