Algebraic properties of the monopole formula

Abstract

The monopole formula provides the Hilbert series of the Coulomb branch for a 3-dimensional N=4 gauge theory. Employing the concept of a fan defined by the matter content, and summing over the corresponding collection of monoids, allows the following: firstly, we provide explicit expressions for the Hilbert series for any gauge group. Secondly, we prove that the order of the pole at t=1 and t=infinity equals the complex or quaternionic dimension of the moduli space, respectively. Thirdly, we determine all bare and dressed BPS monopole operators that are sufficient to generate the entire chiral ring. As an application, we demonstrate the implementation of our approach to computer algebra programs and the applicability to higher rank gauge theories.

arXiv commentv2: 37 pages, 7 figures, 6 tables; matches JHEP version

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Cited by in corpus (10)

• Branes and the Kraft-Procesi transition: classical case
• Mirror symmetry and line operators
• Quiver Theories and Formulae for Nilpotent Orbits of Exceptional Algebras
• Discrete quotients of 3-dimensional N = 4 Coulomb branches via the cycle index
• Nilpotent orbits and the Coulomb branch of $T^{\sigma }(G)$ theories: special orthogonal vs orthogonal gauge group factors
• Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional N=4 theories
• Nonabelian Mirror Symmetry Beyond the Chiral Ring
• Actions on the quiver -- Discrete quotients on the Coulomb branch
• Nilpotent orbit Coulomb branches of types AD
• HWG for Coulomb branch of $3d$ Sicilian theory mirrors