Nilpotent orbit Coulomb branches of types AD

Abstract

We develop a new method for constructing $3d$ $\mathcal{N}=4$ Coulomb branch chiral rings in terms of gauge-invariant generators and relations while making the global symmetry manifest. Our examples generalise to all balanced quivers of type $A$ and $D$ whose Coulomb branches are closures of nilpotent orbits. This new approach is a synthesis of operator counting using Hilbert series and explicit algebraic construction introduced by Bullimore, Dimofte and Gaiotto with significant potential for further generalisation to other quivers, including non-simply laced. The method also identifies complex mass deformations of many Coulomb branches, providing an explicit construction for complex deformations of nilpotent orbits.

arXiv comment38 pages

References in corpus (20)

• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Mirror Symmetry in Three Dimensional Gauge Theories
• New Phenomena in SU(3) Supersymmetric Gauge Theory
• Counting Gauge Invariants: the Plethystic Program
• Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
• Topological Disorder Operators in Three-Dimensional Conformal Field Theory
• Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories
• Monopole Operators and Mirror Symmetry in Three Dimensions
• Coulomb Branch and The Moduli Space of Instantons
• 3d Coulomb branch and 5d Higgs branch at infinite coupling
• Quiver Subtractions
• Instanton Operators and the Higgs Branch at Infinite Coupling
• Quiver Theories for Moduli Spaces of Classical Group Nilpotent Orbits
• The Infrared Physics of Bad Theories
• Quiver Theories and Formulae for Nilpotent Orbits of Exceptional Algebras
• The Infrared Fixed Points of 3d $\mathcal{N}=4$ $USp(2N)$ SQCD Theories
• Discrete Gauging in Coulomb branches of Three Dimensional $\mathcal{N}=4$ Supersymmetric Gauge Theories
• Algebraic properties of the monopole formula
• Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional N=4 theories
• Ring Relations and Mirror Map from Branes

Cited by in corpus (6)

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• Nonabelian Mirror Symmetry Beyond the Chiral Ring
• Atomic Higgsings of 6D SCFTs
• Quantized Coulomb Branches, Monopole Bubbling and Wall-Crossing Phenomena in 3d $\mathcal{N}=4$ Theories