On Gauge Enhancement and Singular Limits in $G_2$ Compactifications of M-theory

TL;DR

This paper investigates the relationship between singular limits and gauge enhancement in $G_2$ compactifications of M-theory, focusing on associative and coassociative submanifolds to understand non-abelian gauge symmetry emergence.

Contribution

It introduces a novel approach linking associative submanifolds to gauge enhancement, providing new insights into singular limits in $G_2$ compactifications.

Findings

Associative submanifolds can indicate non-abelian gauge symmetry points.

Gauge enhancement scenarios relate to calibrated submanifolds and conifold transitions.

The study offers examples illustrating these gauge enhancement mechanisms.

Abstract

We study the physics of singular limits of $G_2$ compactifications of M-theory, which are necessary to obtain a compactification with non-abelian gauge symmetry or massless charged particles. This is more difficult than for Calabi-Yau compactifications, due to the absence of calibrated two-cycles that would have allowed for direct control of W-boson masses as a function of moduli. Instead, we study the relationship between gauge enhancement and singular limits in $G_2$ moduli space where an associative or coassociative submanifold shrinks to zero size; this involves the physics of topological defects and sometimes gives indirect control over particle masses, even though they are not BPS. We show how a lemma of Joyce associates the class of a three-cycle to any $U(1)$ gauge theory in a smooth $G_2$ compactification. If there is an appropriate associative submanifold in this class then in the limit of nonabelian gauge symmetry it may be interpreted as a gauge theory worldvolume and provides the location of the singularities associated with non-abelian gauge or matter fields. We identify a number of gauge enhancement scenarios related to calibrated submanifolds, including Coulomb branches and non-isolated conifolds, and also study examples that realize them.