Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n

Abstract

We study chiral gauge-invariant operators on moduli spaces of G instantons for any classical group G on A-type ALE spaces using Hilbert Series (HS). Moduli spaces of instantons on an ALE space can be realized as Higgs branches of certain quiver gauge theories which appear as world-volume theories on Dp branes in a Dp-D(p+4) system with the D(p+4) branes (with or without O(p+4) planes) wrapping the ALE space. We study in detail a list of quiver gauge theories which are related to G-instantons of arbitrary ranks and instanton numbers on a generic A_{n-1} ALE space and discuss the corresponding brane configurations. For a large class of theories, we explicitly compute the Higgs branch HS which reveals various algebraic/geometric aspects of the moduli space such as the dimension of the space, generators of the moduli space and relations connecting them. In a large number of examples involving lower rank instantons, we demonstrate that HS for equivalent instantons of isomorphic gauge groups but very different quiver descriptions do indeed agree, as expected.

88 pages with 20 pages of Appendices; 45 figures

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