A Note on Fluxes and Superpotentials in M-theory Compactifications on Manifolds of G_2 Holonomy

TL;DR

This paper examines how G-flux in M-theory compactified on G_2 manifolds breaks N=1 supersymmetry, validating Gukov's superpotential proposal by comparing it with supergravity-derived potentials.

Contribution

It confirms Gukov's superpotential accurately captures supersymmetry breaking effects, including fluxes transverse to the compactification manifold.

Findings

Superpotential W matches the bosonic potential from supergravity.

W depends on G-flux on X and transverse to X.

Validation of superpotential's role in supersymmetry breaking.

Abstract

We consider the breaking of N=1 supersymmetry by non-zero G-flux when M-theory is compactified on a smooth manifold X of G_2 holonomy. Gukov has proposed a superpotential W to describe this breaking in the low-energy effective theory. We check this proposal by comparing the bosonic potential implied by W with the corresponding potential deduced from the eleven-dimensional supergravity action. One interesting aspect of this check is that, though W depends explicitly only on G-flux supported on X, W also describes the breaking of supersymmetry by G-flux transverse to X.