Calibrated Geometries and Non Perturbative Superpotentials in M-Theory

TL;DR

This paper explores non-perturbative superpotentials in M-theory compactifications on G_2 manifolds, using calibrated geometry and supergravity to compute effects from membranes wrapped on supersymmetric cycles.

Contribution

It introduces a method to calculate superpotentials from membrane instantons using calibrated geometries in G_2 holonomy manifolds, linking supergravity and geometric approaches.

Findings

Superpotentials from membranes on associative submanifolds are computed.

Calibrated geometry provides a framework for non-perturbative effects.

Supergravity compactification yields consistent superpotential calculations.

Abstract

We consider non perturbative effects in M-theory compactifications on a seven-manifold of G_2 holonomy arising from membranes wrapped on supersymmetric three-cycles. When membranes are wrapped on associative submanifolds they induce a superpotential that can be calculated using calibrated geometry. This superpotential is also derived from compactification on a seven-manifold, to four dimensional Anti-de Sitter spacetime, of eleven dimensional supergravity with non vanishing expectation value of the four-form field strength.