  The known supergravity solution for wrapped D5-branes on the two-cycle of a
Kahler resolved conifold is in general ISD but not supersymmetric, with the
supersymmetry being broken by the presence of (1, 2) fluxes. However if we
allow a non-Kahler metric on the resolved conifold, supersymmetry can easily be
restored. The vanishing of the (1, 2) fluxes here corresponds to, under certain
conformal rescalings of the metric, the torsion class constraints. We construct
a class of explicit non-Kahler metrics on the resolved conifold satisfying the
constraints. All this can also be studied from M-theory, where the fluxes and
branes become non-localized G-fluxes on deformed Taub-NUT spaces.
Interestingly, the gauge fluctuations on the wrapped D5-branes appear now as
localized G-fluxes in M-theory. These localized fluxes are related to certain
harmonic two-forms that are normalizable. We compute these forms explicitly and
discuss how new constraints on the geometry of the non-Kahler manifolds may
appear from M-theory considerations.
