Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional N=4 theories

Abstract

The Coulomb branches of certain 3-dimensional N=4 quiver gauge theories are closures of nilpotent orbits of classical or exceptional algebras. The monopole formula, as Hilbert series of the associated Coulomb branch chiral ring, has been successful in describing the singular hyper-Kähler structure. By means of the monopole formula with background charges for flavour symmetries, which realises real mass deformations, we study the resolution properties of all (characteristic) height two nilpotent orbits. As a result, the monopole formula correctly reproduces (i) the existence of a symplectic resolution, (ii) the form of the symplectic resolution, and (iii) the Mukai flops in the case of multiple resolutions. Moreover, the (characteristic) height two nilpotent orbit closures are resolved by cotangent bundles of Hermitian symmetric spaces and the unitary Coulomb branch quiver realisations exhaust all the possibilities.

v2: 29 pages, 11 tables, 1 figure, matches JHEP version

References in corpus (17)

• Counting Gauge Invariants: the Plethystic Program
• Supersymmetry enhancement by monopole operators
• Coulomb Branch and The Moduli Space of Instantons
• Counting Chiral Operators in Quiver Gauge Theories
• T^σ_ρ(G) Theories and Their Hilbert Series
• Coulomb branch Hilbert series and Hall-Littlewood polynomials
• Branes and the Kraft-Procesi Transition
• Coulomb branch Hilbert series and Three Dimensional Sicilian Theories
• Highest Weight Generating Functions for Hilbert Series
• Branes and the Kraft-Procesi transition: classical case
• Quiver Theories and Formulae for Nilpotent Orbits of Exceptional Algebras
• The moduli spaces of $3d$ $\mathcal{N}\ge 2$ Chern-Simons gauge theories and their Hilbert series
• Nilpotent orbits and the Coulomb branch of $T^{\sigma }(G)$ theories: special orthogonal vs orthogonal gauge group factors
• Algebraic properties of the monopole formula
• Birational geometry of symplectic resolutions of nilpotent orbits II
• Describing codimension two defects
• Normaliz 2013-2016

Cited by in corpus (8)

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• Manifestly Covariant Worldline Actions from Coadjoint Orbits. Part I: Generalities and Vectorial Descriptions
• Minimally Unbalanced Quivers
• Nilpotent orbit Coulomb branches of types AD
• Masses, Sheets and Rigid SCFTs
• Atomic Higgsings of 6D SCFTs
• $D_n$ Dynkin quiver moduli spaces
• Crystal bases and three-dimensional $\mathcal{N}=4$ Coulomb branches