G2-manifolds with parallel characteristic torsion

Abstract

We classify 7-dimensional cocalibrated G 2 -manifolds with parallel characteristic torsion and non-abelian holonomy. All these spaces admit a metric connection ∇ c with totally skew-symmetric torsion and a spinor field Ψ 1 solving the equations in the common sector of type II superstring theory. There exist G 2 -structures with parallel characteristic torsion that are not naturally reductive.