Fivebranes wrapped on associative three-cycles

We construct supergravity solutions corresponding to fivebranes wrapping associative three-cycles of constant curvature in manifolds of $G_2$-holonomy. The solutions preserve 2 supercharges and are first constructed in $D=7\mathrm{}$ gauged supergravity and then lifted to $D=10,11.\mathrm{}$ 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 $D=3\mathrm{}$ by exhibiting a flow to an ${\mathrm{AdS}}_4$ region. For IIB-fivebranes wrapped on a three-sphere we speculate on a connection with spontaneous supersymmetry breaking of pure $\mathcal{N}=1\mathrm{}$ super Yang-Mills theory in $D=3.\mathrm{}$