M theory and Singularities of Exceptional Holonomy Manifolds

TL;DR

This paper reviews recent advances in understanding singularities in G_2 and Spin(7) holonomy manifolds within M theory, highlighting their role in modeling realistic particle physics and strongly coupled gauge theories.

Contribution

It develops techniques to analyze M theory physics near singularities in exceptional holonomy manifolds and connects these to properties of three-dimensional gauge theories.

Findings

Singularities enable non-Abelian gauge groups and chiral fermions in M theory compactifications.

Methods to study M theory near singularities have advanced understanding of gauge theory phenomena.

Insights into confinement, mass gap, and phase transitions in strongly coupled gauge theories.

Abstract

M theory compactifications on G_2 holonomy manifolds, whilst supersymmetric, require singularities in order to obtain non-Abelian gauge groups, chiral fermions and other properties necessary for a realistic model of particle physics. We review recent progress in understanding the physics of such singularities. Our main aim is to describe the techniques which have been used to develop our understanding of M theory physics near these singularities. In parallel, we also describe similar sorts of singularities in Spin(7) holonomy manifolds which correspond to the properties of three dimensional field theories. As an application, we review how various aspects of strongly coupled gauge theories, such as confinement, mass gap and non-perturbative phase transitions may be given a simple explanation in M theory.