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

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.

Published version

References in corpus (6)

• Gauge Theory at Large N and New G_2 Holonomy Metrics
• New Complete Non-compact Spin(7) Manifolds
• Non-Perturbative Superpotentials from Membrane Instantons in Heterotic M-Theory
• Duality and Fibrations on G_2 Manifolds
• Dynamical emergence of extra dimensions and warped geometries
• Resolved Branes and M-theory on Special Holonomy Spaces

Cited by in corpus (4)

• Brane Solitons for G_2 Structures in Eleven-Dimensional Supergravity Re-Visited
• A construction of G_2 holonomy spaces with torus symmetry
• New G2 holonomy metrics, D6 branes with inherent U(1)xU(1) isometry and gamma-deformations
• Supersymmetry of Noncompact MQCD-like Membrane Instantons and Heat Kernel Asymptotics