Moduli spaces of G2 manifolds

TL;DR

This review summarizes recent mathematical progress on the moduli spaces of G2 manifolds, which are 7-dimensional structures with special holonomy, important in both geometry and theoretical physics.

Contribution

It provides a comprehensive overview of the current state of research on G2 moduli spaces, including deformation theory and local geometric properties.

Findings

Overview of G2 manifold basics

Analysis of local deformation theory

Insights into the local geometry of moduli spaces

Abstract

This paper is a review of current developments in the study of moduli spaces of G2 manifolds. G2 manifolds are 7-dimensional manifolds with the exceptional holonomy group G2. Although they are odd-dimensional, in many ways they can be considered as an analogue of Calabi-Yau manifolds in 7 dimensions. They play an important role in physics as natural candidates for supersymmetric vacuum solutions of M-theory compactifications. Despite the physical motivation, many of the results are of purely mathematical interest. Here we cover the basics of G2 manifolds, local deformation theory of G2 structures and the local geometry of the moduli spaces of G2 structures.