Aspects of the moduli space of instantons on CP^2 and its orbifolds

Abstract

We study the moduli space of (framed) self-dual instantons on CP 2 . These are described by an ADHM-like construction which allows to compute the Hilbert series of the moduli space. The latter has been found to be blind to certain compact directions. In this paper we probe these, finding them to correspond to a Grassmanian, upon considering appropriate ungaugings. Moreover, the ADHM-like construction can be embedded into a 3d gauge theory with a known gravity dual. Using this, we realize in AdS4/CF T3 (part of) the instanton moduli space providing at the same time further evidence supporting the AdS4/CF T3 duality. Moreover, upon orbifolding, we provide the ADHM-like construction of instantons on CP 2 /Zn as well as compute its Hilbert series. As in the unorbifolded case, these turn out to coincide with those for instantons on C 2 /Zn.