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.

v2: 37 pages, 7 figures, 6 tables; matches JHEP version

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Cited by in corpus (3)

• 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
• HWG for Coulomb branch of $3d$ Sicilian theory mirrors