Coulomb Branch and The Moduli Space of Instantons

Abstract

The moduli space of instantons on C^2 for any simple gauge group is studied using the Coulomb branch of N=4 gauge theories in three dimensions. For a given simple group G, the Hilbert series of such an instanton moduli space is computed from the Coulomb branch of the quiver given by the over-extended Dynkin diagram of G. The computation includes the cases of non-simply-laced gauge groups G, complementing the ADHM constructions which are not available for exceptional gauge groups. Even though the Lagrangian description for non-simply laced Dynkin diagrams is not currently known, the prescription for computing the Coulomb branch Hilbert series of such diagrams is very simple. For instanton numbers one and two, the results are in agreement with previous works. New results and general features for the moduli spaces of three and higher instanton numbers are reported and discussed in detail.

32 pages + Appendices. v2: typos corrected

References in corpus (6)

• Counting Gauge Invariants: the Plethystic Program
• Supersymmetry enhancement by monopole operators
• Superconformal indices of three-dimensional theories related by mirror symmetry
• Down the rabbit hole with theories of class S
• Coulomb branch Hilbert series and Hall-Littlewood polynomials
• Coulomb branch Hilbert series and Three Dimensional Sicilian Theories

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