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The spinorial geometry of supersymmetric heterotic string backgrounds
- Source :
- Journal of High Energy Physics. 2006:063-063
- Publication Year :
- 2006
- Publisher :
- Springer Science and Business Media LLC, 2006.
-
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 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.<br />Comment: 73pp. v2: minor changes
- Subjects :
- High Energy Physics - Theory
Mathematics - Differential Geometry
Physics
Nuclear and High Energy Physics
Spinor
Null (mathematics)
Holonomy
FOS: Physical sciences
Geometry
Riemannian manifold
Principal bundle
General Relativity and Quantum Cosmology
High Energy Physics - Theory (hep-th)
Differential Geometry (math.DG)
Killing spinor
Lie algebra
FOS: Mathematics
Mathematics::Differential Geometry
Connection (algebraic framework)
Subjects
Details
- ISSN :
- 10298479
- Volume :
- 2006
- Database :
- OpenAIRE
- Journal :
- Journal of High Energy Physics
- Accession number :
- edsair.doi.dedup.....69cd19935044cd686182b0392d1164b7