D6-branes wrapping Kähler four-cycles

We construct supergravity duals of D6-branes wrapping Kähler four-cycles inside a Calabi–Yau threefold, CY3. We obtain the purely gravitational M-theory description, which turns out to be a Calabi–Yau fourfold, CY4. We also analyze the dynamics of a probe D6 in this background.