Hasse Diagrams for $3d$ $\mathcal{N}=4$ Quiver Gauge Theories -- Inversion and the full Moduli Space

Abstract

We study Hasse diagrams of moduli spaces of $3d$ $\mathcal{N}=4$ quiver gauge theories. The goal of this work is twofold: 1) We introduce the notion of inverting a Hasse diagram and conjecture that the Coulomb branch and Higgs branch Hasse diagrams of certain theories are related through this operation. 2) We introduce a Hasse diagram to map out the entire moduli space of the theory, including the Coulomb, Higgs and mixed branches. For theories whose Higgs and Coulomb branch Hasse diagrams are related by inversion it is straight forward to generate the Hasse diagram of the entire moduli space. We apply inversion of the Higgs branch Hasse diagram in order to obtain the Coulomb branch Hasse diagram for bad theories and obtain results consistent with the literature. For theories whose Higgs and Coulomb branch Hasse diagrams are not related by inversion it is nevertheless possible to produce the Hasse diagram of the full moduli space using different methods. We give examples for Hasse diagrams of the entire moduli space of theories with \emph{enhanced} Coulomb branches.

References in corpus (6)

• T^σ_ρ(G) Theories and Their Hilbert Series
• Branes and the Kraft-Procesi Transition
• Magnetic Quivers, Higgs Branches, and 6d N=(1,0) Theories -- Orthogonal and Symplectic Gauge Groups
• Magnetic Quivers from Brane Webs with O5 Planes
• Quiver Theories and Hilbert Series of Classical Slodowy Intersections
• Hilbert series and mixed branches of $T[SU(N)]$ theory

Cited by in corpus (23)

• Coulomb and Higgs Branches from Canonical Singularities: Part 0
• (5d RG-flow) Trees in the Tropical Rain Forest
• (Symplectic) Leaves and (5d Higgs) Branches in the Poly(go)nesian Tropical Rain Forest
• S-fold magnetic quivers
• Magnetic Lattices for Orthosymplectic Quivers
• Connecting 5d Higgs Branches via Fayet-Iliopoulos Deformations
• Towards a classification of rank $r$ $\mathcal{N}=2$ SCFTs Part II: special Kahler stratification of the Coulomb branch
• Magnetic quivers for rank 2 theories
• Fibrations and Hasse diagrams for 6d SCFTs
• Folding Orthosymplectic Quivers
• Higgs Branches of U/SU Quivers via Brane Locking
• Magnetic quivers and line defects -- On a duality between 3d N=4 unitary and orthosymplectic quivers
• Hierarchy of RG flows in 6d $(1,0)$ orbi-instantons
• Coulomb Branch Global Symmetry and Quiver Addition
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Discrete gauging and Hasse diagrams
• Orthosymplectic Implosions
• On non-supersymmetric fixed points in five dimensions
• Orthosymplectic Quotient Quiver Subtraction
• Actions on the quiver -- Discrete quotients on the Coulomb branch
• Quiver Polymerisation
• Crystal bases and three-dimensional $\mathcal{N}=4$ Coulomb branches
• FI-flows of 3d N=4 Theories