Fivebranes wrapped on associative three-cycles

We construct supergravity solutions corresponding to fivebranes wrapping associative three-cycles of constant curvature in manifolds of G₂-holonomy. The solutions preserve 2 supercharges and are first constructed in $D=7$ gauged supergravity and then lifted to $D=10,11.$ We show that the low-energy theory of M-fivebranes wrapped on a compact hyperbolic three-space is dual to a superconformal field theory in $D=3$ by exhibiting a flow to an AdS₄ region. For IIB-fivebranes wrapped on a three-sphere we speculate on a connection with spontaneous supersymmetry breaking of pure N=1 super Yang-Mills theory in $D=3.$