The ADHM-like constructions for instantons on CP 2 and three-dimensional gauge theories

摘要

We study the moduli spaces of self-dual instantons on CP 2 in a simple group G . When G is a classical group, these instanton solutions can be realized using ADHM-like constructions which can be naturally embedded into certain three-dimensional quiver gauge theories with four supercharges. The topological data for such instanton bundles and their relations to the quiver gauge theories are described. Based on such gauge theory constructions, we compute the Hilbert series of the moduli spaces of instantons that correspond to various configurations. The results turn out to be equal to the Hilbert series of their counterparts on C 2 upon an appropriate mapping. We check the former against the Hilbert series derived from the blowup formula for the Hirzebruch surface F 1 and find an agreement. The connection between the moduli spaces of instantons on such two spaces is explained in detail.