M-theory on manifolds of G2 holonomy: the first twenty years

TL;DR

This paper reviews the development of G2 holonomy manifolds in M-theory over twenty years, highlighting their role in supersymmetry preservation, compactification, and realistic model building.

Contribution

It provides a comprehensive overview of G2 holonomy manifolds in M-theory, emphasizing their significance in supersymmetry and model construction over two decades.

Findings

G2 manifolds enable N=1 supersymmetry in 4D.

Singular G2 compactifications can produce realistic gauge groups.

G2 holonomy remains central in M-theory dualities and model building.

Abstract

In 1981, covariantly constant spinors were introduced into Kaluza-Klein theory as a way of counting the number of supersymmetries surviving compactification. These are related to the holonomy group of the compactifying manifold. The first non-trivial example was provided in 1982 by D=11 supergravity on the squashed S7, whose G2 holonomy yields N=1 in D=4. In 1983, another example was provided by D=11 supergravity on K3, whose SU(2) holonomy yields half the maximum supersymmetry. In 2002, G2 and K3 manifolds continue to feature prominently in the full D=11 M-theory and its dualities. In particular, singular G2 compactifications can yield chiral (N=1,D=4) models with realistic gauge groups. The notion of generalized holonomy is also discussed.