Kahler Potential for M-theory on a G_2 Manifold

TL;DR

This paper calculates the Kahler potential for M-theory compactified on G_2 manifolds with small torsion, providing explicit formulas and verifying them through direct integration, and discusses effects of singularities.

Contribution

It introduces a method to compute the Kahler potential for G_2 compactifications using explicit G_2 structures with small torsion, including singularity effects.

Findings

Derived explicit Kahler potential for G_2 manifolds

Verified Kahler metric components via harmonic form integration

Analyzed gauge-kinetic functions with singularities

Abstract

We compute the moduli Kahler potential for M-theory on a compact manifold of G_2 holonomy in a large radius approximation. Our method relies on an explicit G_2 structure with small torsion, its periods and the calculation of the approximate volume of the manifold. As a verification of our result, some of the components of the Kahler metric are computed directly by integration over harmonic forms. We also discuss the modification of our result in the presence of co-dimension four singularities and derive the gauge-kinetic functions for the massless gauge fields that arise in this case.