Branes wrapped on coassociative cycles

Abstract We obtain a supergravity solution arising when D6-branes are wrapped on coassociative four-cycles of constant curvature in seven manifolds of G 2 holonomy. The solutions preserve two supercharges and thus represent supergravity duals of three-dimensional Yang–Mills with N =1 supersymmetry. When uplifted to eleven dimensions our solution describes M-theory on the background of an eight manifold with spin(7) holonomy.