Quiver Subtraction on the Higgs Branch

TL;DR

This paper develops a classification and subtraction algorithm for Higgs branches in simply-laced unitary quiver gauge theories, revealing detailed Higgsing patterns and global symmetry properties.

Contribution

It introduces a Higgs branch subtraction algorithm that classifies Higgsing patterns and determines global symmetries, including sensitivity to monodromies and Weyl groups.

Findings

Classified all Higgsing patterns for the theories.

Developed an algorithm sensitive to global topological data.

Verified Higgs branches as slices in nilpotent cones.

Abstract

This paper classifies all Higgs branch Higgsing patterns for simply-laced unitary quiver gauge theories with eight supercharges (including multiple loops) and introduces a Higgs branch subtraction algorithm. All possible minimal transitions are given, identifying differences between slices that emerge on the Higgs and Coulomb branches. In particular, the algorithm is sensitive to global information including monodromies and Namikawa-Weyl groups. Guided by symplectic duality, the algorithm further determines the global symmetry on the Coulomb branch, and verifies the exclusion of $C$ type or $F_4$ global symmetry for (simply-laced) unitary quiver gauge theories. The Higgs branches of some unitary quivers are verified to give slices in the nilpotent cones of exceptional simple Lie algebras.