Local geometry of the G2 moduli space

TL;DR

This paper investigates the local geometry of the G2 moduli space by analyzing deformations of torsion-free G2 structures, computing higher-order expansions, and relating the curvature of the moduli space to physical couplings in M-theory compactifications.

Contribution

It provides a detailed expansion of the Hodge star of the G2 3-form to fourth order and derives the full curvature of the moduli space metric, connecting geometric and physical aspects.

Findings

Expanded the Hodge star of the G2 form to fourth order in deformations

Derived the full curvature of the G2 moduli space metric

Connected the curvature to the Yukawa coupling in M-theory

Abstract

We consider deformations of torsion-free G2 structures, defined by the G2-invariant 3-form $\phi$ and compute the expansion of the Hodge star of $\phi$ to fourth order in the deformations of $\phi$. By considering M-theory compactified on a G2 manifold, the G2 moduli space is naturally complexified, and we get a Kahler metric on it. Using the expansion of the Hodge star of $\phi$ we work out the full curvature of this metric and relate it to the Yukawa coupling.