Supersymmetric M3-branes and G2 manifolds

We obtain a generalisation of the original complete Ricci-flat metric of G(2) holonomy on R-4 x S-3 to a family with a nontrivial parameter lambda. For generic lambda the solution is singular, but it is regular when lambda = {- 1, 0, +1}. The case lambda = 0 corresponds to the original G(2) metric, and lambda = {-1, 1} are related to this by an S-3 automorphism of the SU(2)(3) isometry group that acts on the S-3 x S-3 principal orbits. We then construct explicit supersymmetric M3-brane solutions in D = 11 supergravity, where the transverse space is a deformation of this class of G(2) metrics. These are solutions of a system of first-order differential equations coming from a superpotential. We also find M3-branes in the deformed backgrounds of new G(2) holonomy metrics that include one found by A. Brandhuber, J. Gomis, S. Gubser and S. Gukov, and show that they also are supersymmetric. (C) 2002 Published by Elsevier Science B.V.