Hilbert series for moduli spaces of two instantons View Full Text


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Article Info

DATE

2013-01

AUTHORS

Amihay Hanany, Noppadol Mekareeya, Shlomo S. Razamat

ABSTRACT

The Hilbert Series (HS) of the moduli space of two G instantons on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{\mathbb{C}}^2} $\end{document}, where G is a simple gauge group, is studied in detail. For a given G, the moduli space is a singular hyperKähler cone with a symmetry group U(2) × G, where U(2) is the natural symmetry group of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{\mathbb{C}}^2} $\end{document}. Holomorphic functions on the moduli space transform in irreducible representations of the symmetry group and hence the Hilbert series admits a character expansion. For cases that G is a classical group (of type A, B, C, or D), there is an ADHM construction which allows us to compute the HS explicitly using a contour integral. For cases that G is of E-type, recent index results allow for an explicit computation of the HS. The character expansion can be expressed as an infinite sum which lives on a Cartesian lattice that is generated by a small number of representations. This structure persists for all G and allows for an explicit expressions of the HS to all simple groups. For cases that G is of type G2 or F4, discrete symmetries are enough to evaluate the HS exactly, even though neither ADHM construction nor index is known for these cases. More... »

PAGES

70

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URI

http://scigraph.springernature.com/pub.10.1007/jhep01(2013)070

DOI

http://dx.doi.org/10.1007/jhep01(2013)070

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1046707518


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