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.
Cite
@article{arxiv.1309.0812,
title = {Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n},
author = {Anindya Dey and Amihay Hanany and Noppadol Mekareeya and Diego Rodriguez-Gomez and Rak-Kyeong Seong},
journal= {arXiv preprint arXiv:1309.0812},
year = {2014}
}
Comments
88 pages with 20 pages of Appendices; 45 figures