Parallel spinors and connections with skew-symmetric torsion in string theory
Abstract
We describe all almost contact metric, almost hermitian and G_2-structures admitting a connection with totally skew-symmetric 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.