Calibrated geometries and non-perturbative superpotentials in M-theory

We consider non-perturbative effects in M-theory compactifications on a sev en-manifold of G(2) holonomy arising from membranes wrapped on supersymmetr ic three-cycles. When membranes are wrapped on associative submanifolds the y induce a superpotential that can be calculated using calibrated geometry. This superpotential is also derived from compactification oil a seven-mani fold, to four dimensional anti-dc Sitter spacetime, of eleven dimensional s upergravity with non-vanishing expectation value of the four-form field str ength.