On the Exact Evaluation of the Membrane Instanton Superpotential in M-Theory on G_2-Holonomy Manifold

TL;DR

This paper systematically evaluates the nonperturbative superpotential contribution from a single M2 brane wrapping a supersymmetric 3-cycle in G_2-holonomy manifolds, extending previous work and analyzing UV divergences related to supersymmetry.

Contribution

It extends the evaluation of membrane instanton effects to non-rigid cycles and explores the UV divergence structure, linking M-theory instantons to topological string dualities.

Findings

Confirmed partial cancellation of UV divergences due to supersymmetry

Extended Harvey and Moore's work to non-rigid cycles

Provided insights into M-theory and topological string duality

Abstract

Following the work of Lima et al on the exact evaluation of the nonperturbative contribution to the superpotential from open-membrane instanton in Heterotic M-Theory, we evaluate systematically the contribution to the superpotential of a membrane instanton obtained by wrapping of a single M2 brane, 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 and Moore. We also do a heat-kernel asymptotics analysis to see whether one gets similar UV-divergent terms for (one or both of) the bosonic and fermionic determinants indicative of (partial) cancelation among them. The answer is in the affirmative, as expected by the supersymmetry of the starting membrane action. This work is a first step, both, in extending the work of Harvey and Moore to the evaluation of nonperturbative superpotentials for non-rigid supersymmetric 3-cycle wrappings, and in understanding the large N Chern-Simons/closed type-A topological string theory duality of Gopakumar and Vafa from M theory point of view.