Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-10-20
JHEP 0602:063,2006
Physics
High Energy Physics
High Energy Physics - Theory
73pp. v2: minor changes
Scientific paper
10.1088/1126-6708/2006/02/063
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 NS$\otimes$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 $K\ltimes\bR^8$ in $Spin(9,1)$, for $K=Spin(7)$, SU(4), $Sp(2)$, $SU(2)\times SU(2)$ 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 $\hat\nabla$-parallel vector field while the latter admit a timelike and two, three, five and nine spacelike $\hat\nabla$-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 $\lambda$ which determines the non-horizontal part of the spacetime metric and of $H$. The curvature of $\lambda$ 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.
Gran Ulf
Lohrmann Philipp
Papadopoulos George
No associations
LandOfFree
The spinorial geometry of supersymmetric heterotic string backgrounds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The spinorial geometry of supersymmetric heterotic string backgrounds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The spinorial geometry of supersymmetric heterotic string backgrounds will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-475705