Superpotentials and Membrane Instantons

TL;DR

This paper studies nonperturbative membrane effects in M-theory compactifications on G2 manifolds, showing they generate superpotential corrections via topological invariants, impacting stability and providing new counting formulas for cycles.

Contribution

It demonstrates that membrane instantons induce superpotential corrections in G2 compactifications and introduces a topological field theory framework for membrane physics.

Findings

Membrane instantons generate superpotential corrections in G2 compactifications.

Superpotential is expressed via topological invariants of 3-cycles.

Derived a counting formula for supersymmetric 3-cycles using mirror symmetry.

Abstract

We investigate nonperturbative effects in M-theory compactifications arising from wrapped membranes. In particular, we show that in $d=4, \mathcal{N}=1$ compactifications along manifolds of $G_2$ holonomy, membranes wrapped on rigid supersymmetric 3-cycles induce nonzero corrections to the superpotential. Thus, membrane instantons destabilize many M-theory compactifications. Our computation shows that the low energy description of membrane physics is usefully described in terms of three-dimensional topological field theories, and the superpotential is expressed in terms of topological invariants of the 3-cycle. We discuss briefly some applications of these results. For example, using mirror symmetry we derive a counting formula for supersymmetric three-cycles in certain Calabi-Yau manifolds.