Coulomb Branch Global Symmetry and Quiver Addition

TL;DR

This paper introduces a method to construct 3d N=4 quivers with enhanced Coulomb branch global symmetry, addressing limitations of existing algorithms based on balanced gauge nodes, and provides examples to improve symmetry identification.

Contribution

It presents a new construction of quivers where the Coulomb branch symmetry exceeds predictions from the balance algorithm, aiding the development of more accurate symmetry detection methods.

Findings

Constructed families of quivers with enhanced global symmetry.

Demonstrated limitations of the balance algorithm in symmetry prediction.

Provided examples for testing improved symmetry algorithms.

Abstract

To date, the best effort made to simply determine the Coulomb branch global symmetry of a theory from a $3d$ $\mathcal{N}=4$ quiver is by applying an algorithm based on its balanced gauge nodes. This often gives the full global symmetry, but there have been many cases seen where it instead gives only a subgroup. This paper presents a method for constructing several families of $3d$ $\mathcal{N}=4$ unitary quivers where the true global symmetry is enhanced from that predicted by the balance algorithm, motivated by the study of Coulomb branch Hasse diagrams. This provides a rich list of examples on which to test improved algorithms for unfailingly identifying the Coulomb branch global symmetry from a quiver.