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Following the work of Lima et al on the exact evaluation of thenonperturbative contribution to the superpotential from open-membrane instantonin Heterotic M-Theory, we evaluate systematically the contribution to thesuperpotential of a membrane instanton obtained by wrapping of a single M2brane, once, on an isolated supersymmetric 3-cycle in a G_2-holonomy manifold.We then try to relate the results obtained to those sketched out in Harvey andMoore. We also do a heat-kernel asymptotics analysis to see whether one getssimilar UV-divergent terms for (one or both of) the bosonic and fermionicdeterminants indicative of (partial) cancelation among them. The answer is inthe affirmative, as expected by the supersymmetry of the starting membraneaction. This work is a first step, both, in extending the work of Harvey andMoore to the evaluation of nonperturbative superpotentials for non-rigidsupersymmetric 3-cycle wrappings, and in understanding the large NChern-Simons/closed type-A topological string theory duality of Gopakumar andVafa from M theory point of view.Comment: Published versio

On the Exact Evaluation of the Membrane Instanton Superpotential in M-Theory onG2-Holonomy Manifold

On the Exact Evaluation of the Membrane Instanton Superpotential in M-Theory onG₂-Holonomy Manifold