Classification and Moduli Kahler Potentials of G_2 Manifolds

TL;DR

This paper classifies orbifold groups for constructing G_2 manifolds and derives the corresponding moduli Kähler potential in M-theory compactifications, advancing understanding of their geometric and physical properties.

Contribution

It provides a classification of orbifold groups and explicitly derives the moduli Kähler potential for G_2 manifolds with blown-up singularities.

Findings

Classification of possible orbifold groups for G_2 manifolds

Explicit derivation of the moduli Kähler potential

Framework for analyzing M-theory compactifications on these manifolds

Abstract

Compact manifolds of G_2 holonomy may be constructed by dividing a seven-torus by some discrete symmetry group and then blowing up the singularities of the resulting orbifold. We classify possible group elements that may be used in this construction and use this classification to find a set of possible orbifold groups. We then derive the moduli Kahler potential for M-theory on the resulting class of G_2 manifolds with blown up co-dimension four singularities.