Properties of moduli spaces of supersymmetric quiver gauge theories with 8 supercharges
File(s)
Author(s)
Li, Chunhao
Type
Thesis
Abstract
The thesis focuses on the study of moduli spaces of 3d N = 4 supersymmetric field theories.
Two aspects are emphasized. Firstly, discrete quotients of the Coulomb branch are studied.
Secondly, the Hasse diagram for Higgs branches are studied. Both aspects are given by
diagrammatic operations on the quiver diagrams.
In the Introduction and Background part, the framework of supersymmetry and the nec
essary mathematics underlying the following two chapters are introduced at a pedagogical
level.
In the second part, it is shown that two families of quivers, the quivers with complete
graphs and the quivers with multiple adjoint loops, have Coulomb branches related by
a quotient of a permutation symmetry. Quotient of cyclic groups is also studied. The
two operations can be combined to generate a quotient by a semi-direct product group of
permutation and cyclic groups. The quotient relations are demonstrated by the Molien
sum and Abelionization process. Examples are included to demonstrate the operations.
In the third part, a bottom to up quiver subtraction algorithm is introduced. The algorithm
can generate the whole Hasse diagram for the Higgs branch of a single-laced unitary quiver.
The interesting feature of the algorithm is that it gives the monodromy of slices around
the leaves. It also calculates the Namikawa Weyl group.
Two aspects are emphasized. Firstly, discrete quotients of the Coulomb branch are studied.
Secondly, the Hasse diagram for Higgs branches are studied. Both aspects are given by
diagrammatic operations on the quiver diagrams.
In the Introduction and Background part, the framework of supersymmetry and the nec
essary mathematics underlying the following two chapters are introduced at a pedagogical
level.
In the second part, it is shown that two families of quivers, the quivers with complete
graphs and the quivers with multiple adjoint loops, have Coulomb branches related by
a quotient of a permutation symmetry. Quotient of cyclic groups is also studied. The
two operations can be combined to generate a quotient by a semi-direct product group of
permutation and cyclic groups. The quotient relations are demonstrated by the Molien
sum and Abelionization process. Examples are included to demonstrate the operations.
In the third part, a bottom to up quiver subtraction algorithm is introduced. The algorithm
can generate the whole Hasse diagram for the Higgs branch of a single-laced unitary quiver.
The interesting feature of the algorithm is that it gives the monodromy of slices around
the leaves. It also calculates the Namikawa Weyl group.
Version
Open Access
Date Issued
2025-10-01
Date Awarded
01/02/2026
Advisor
Hanany, Amihay
Publisher Department
Department of Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)