The role of U(1)'s in 5d theories, Higgs branches, and geometry

TL;DR

This paper investigates the Higgs branches of 5d $ ext{N}=1$ quiver gauge theories using M-theory on local Calabi-Yau threefolds, revealing insights into gauge group structures and the effects of compactification on moduli.

Contribution

It introduces a novel geometric approach to analyze Higgs branches in 5d theories, clarifies the role of U(1) factors, and connects these findings with dual string theory descriptions.

Findings

Compatibility with unitary gauge groups over special unitary groups

Identification of a St"uckelberg mechanism eliminating Abelian factors upon compactification

Provision of missing Higgs branch moduli through geometric and duality analyses

Abstract

We explore the Higgs branches of five-dimensional $\mathcal{N}=1$ quiver gauge theories at finite coupling from the paradigm of M-theory on local Calabi-Yau threefolds described as $\mathbb{C}^\ast$-fibrations over local K3's. By properly counting local deformations of singularities, we find results compatible with unitary as opposed to special unitary gauge groups. We interpret these results by dualizing to both IIA on local K3's with D6-branes, and to IIB with 5-branes. Finally, we find that, by compactifying the $\mathbb{C}^\ast$-fibers to tori, a well-known St\"uckelberg mechanism eliminates Abelian factors, and provides missing Higgs branch moduli in a very interesting way. This is also explained from the dual IIA and IIB viewpoints.