Supersymmetric M3-branes and G2 manifolds Original Research Article

We obtain a generalisation of the original complete Ricci-flat metric of G2 holonomy on R4×S3 to a family with a nontrivial parameter λ. For generic λ the solution is singular, but it is regular when λ={−1,0,+1}. The case λ=0 corresponds to the original G2 metric, and λ={−1,1} are related to this by an S3 automorphism of the SU(2)3 isometry group that acts on the S3×S3 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 G2 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 G2 holonomy metrics that include one found by A. Brandhuber, J. Gomis, S. Gubser and S. Gukov, and show that they also are supersymmetric.