  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.
