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.

Latex2e, 35 pages

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• Conformal foliations, Kähler twists and the Weinstein construction