Discrete quotients of 3-dimensional N = 4 Coulomb branches via the cycle index

Abstract

The study of Coulomb branches of 3-dimensional N=4 gauge theories via the associated Hilbert series, the so-called monopole formula, has been proven useful not only for 3-dimensional theories, but also for Higgs branches of 5 and 6-dimensional gauge theories with 8 supercharges. Recently, a conjecture connected different phases of 6-dimensional Higgs branches via gauging of a discrete global $S_n$ symmetry. On the corresponding 3-dimensional Coulomb branch, this amounts to a geometric $S_n$-quotient. In this note, we prove the conjecture on Coulomb branches with unitary nodes and, moreover, extend it to Coulomb branches with other classical groups. The results promote discrete $S_n$-quotients to a versatile tool in the study of Coulomb branches.

v2: 24 pages, matches JHEP version

References in corpus (12)

• Coulomb Branch and The Moduli Space of Instantons
• 3d Coulomb branch and 5d Higgs branch at infinite coupling
• 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
• Discrete Gauging in Six Dimensions
• The Small $E_8$ Instanton and the Kraft Procesi Transition
• Branes and the Kraft-Procesi transition: classical case
• Quiver Theories and Formulae for Nilpotent Orbits of Exceptional Algebras
• Nilpotent orbits and the Coulomb branch of $T^{\sigma }(G)$ theories: special orthogonal vs orthogonal gauge group factors
• Algebraic properties of the monopole formula

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• Magnetic quivers and negatively charged branes
• Magnetic quivers and line defects -- On a duality between 3d N=4 unitary and orthosymplectic quivers
• Coulomb Branch Global Symmetry and Quiver Addition
• Ungauging Schemes and Coulomb Branches of Non-simply Laced Quiver Theories
• Discrete gauging and Hasse diagrams
• Actions on the quiver -- Discrete quotients on the Coulomb branch
• Complex Symplectic Contractions and 3d Mirrors
• Atomic Higgsings of 6D SCFTs
• Some Open Questions in Quiver Gauge Theory
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