Gauging global symmetries with magnetic quivers
File(s)
Author(s)
Kumaran, Guhesh
Type
Thesis or dissertation
Abstract
In this thesis four techniques which gauge Coulomb branch global symmetry subgroups of 3d N=4 quiver gauge theories are introduced. This is a challenging problem due to the quantum corrections of the Coulomb branch, nevertheless each technique developed here is combinatorial in nature which avoids this issue. Three of the methods are a type of quotient quiver subtraction, involving a subtraction of quiver diagrams, and the fourth is a quiver polymerisation, which involves combining two quivers or forming a loop in one quiver. These methods are derived from either 3d mirror symmetry, or through the analysis of Higgs branches of 6d N=(1,0) or class S theories using magnetic quivers. Mathematically, Coulomb branches of 3d N=4 theories and Higgs branches of theories with eight supercharges are a type of hyper-Kähler variety called a symplectic singularity. The act of gauging a global symmetry subgroup corresponds to performing a hyper-Kähler quotient on the moduli space which results in constructions for new symplectic singularities. After going through some physics and mathematics background for the computations involved, the thesis proceeds by developing each of the four techniques in turn and applying them to a range of physics and mathematical contexts including: moduli spaces of instantons, dualities in 4d N=2 theories, the 6d N=(1,0) (E6,E6) conformal matter theory, and nilpotent orbit closures. These results are supported with computation of Hilbert series.
Version
Open Access
Date Issued
2026-04-16
Date Awarded
2026-07-01
Copyright Statement
Attribution-NonCommercial 4.0 International Licence (CC BY-NC)
License URL
Advisor
Hanany, Amihay
Publisher Department
Department of Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)