Parallel spinors and connections with skewsymmetric torsion in string theory
Abstract
We describe all almost contact metric, almost hermitian and $G_2$structures admitting a connection with totally skewsymmetric torsion tensor, and prove that there exists at most one such connection. We investigate its torsion form, its Ricci tensor, the Dirac operator and the $\nabla$parallel spinors. In particular, we obtain solutions of the type II string in dimension $n=5,6$ and 7.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2001
 arXiv:
 arXiv:math/0102142
 Bibcode:
 2001math......2142F
 Keywords:

 Mathematics  Differential Geometry;
 High Energy Physics  Theory;
 53C25;
 53C27;
 53C55;
 81T30
 EPrint:
 Latex2e, 35 pages