Coulomb Branch and The Moduli Space of Instantons

TL;DR

This paper uses Coulomb branch techniques of 3D N=4 gauge theories to compute the moduli space of instantons on C^2 for various simple gauge groups, including non-simply-laced cases, providing new insights for higher instanton numbers.

Contribution

It introduces a Coulomb branch approach to compute instanton moduli spaces for all simple gauge groups, including cases lacking traditional ADHM constructions.

Findings

Computed Hilbert series for instanton moduli spaces with instanton numbers one and two.

Extended the Coulomb branch method to non-simply-laced gauge groups.

Presented new results for moduli spaces with three or more 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.