Parallel spinors and connections with skew-symmetric torsion in string theory

Details Parallel spinors and connections with skew-symmetric torsion in string theory Parallel spinors and connections with skew-symmetric torsion in string theory

2001-02-19

arxiv.org/abs/math/0102142v5

AsianJ.Math.6:303-336,2002

Mathematics

Differential Geometry

Latex2e, 35 pages

Scientific paper

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.

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