holonomy metrics and wrapped D6-branes
arXiv:hep-th/0608163 · doi:10.1103/PhysRevD.75.065017
Abstract
We determine torsion class constraints for the supergravity background produced by D6-branes wrapping special Lagrangian cycles in a Calabi-Yau 3-fold. We employ a recently introduced method which involves probing the putative background by all possible supersymmetric brane configurations. We then lift this background to 11-dimensions to a product of 4-d Minkowski space and a 7-fold of G2-holonomy. The latter is a particular U(1) bundle over an almost complex manifold of SU(3) structure with specific torsion class constraints. We construct the closed 3- and 4-forms which calibrate the 3- and 4-cycles in the G2-holonomy manifold.
21 pages, references added