ar X iv : h ep - t h / 06 08 16 3 v 3 6 O ct 2 00 6 G 2 holonomy metrics and wrapped D 6 - branes

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 3and 4-forms which calibrate the 3and 4-cycles in the G2-holonomy manifold. HUTP-06/A0034 BCCUNY-HEP /06-04 hep-th/0608163 email: Ansar [email protected] email: [email protected]