M3-branes, G_2 Manifolds and Pseudo-supersymmetry

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Abstract
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 non-trivial 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\times S^3 principal orbits. We also construct explicit 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. They can also be obtained as the integrability conditions for a ``pseudo-supersymmetry'' that arises if one changes a certain coefficient in the the fermionic eleven-dimensional supergravity transformations by a factor of 3/2. 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, with the same modification of the supergravity transformations. Thus, all the examples of M3-branes on deformations of known G_2 holonomy spaces, found in hep-th/0105096 and in this paper, preserve the same pseudo-supersymmetry, suggesting a universality of pseudo-supersymmetry for an extensive class of classical D=4 vacua in M-theory.

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