The Hilbert series of the one instanton moduli space View Full Text


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Article Info

DATE

2010-06-28

AUTHORS

Sergio Benvenuti, Amihay Hanany, Noppadol Mekareeya

ABSTRACT

The moduli space of k 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{R}^4} $\end{document} for a classical gauge group G is known to be given by the Higgs branch of a supersymmetric gauge theory that lives on Dp branes probing D(p + 4) branes in Type II theories. For p = 3, these (3 + 1) dimensional gauge theories have \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} = 2 $\end{document} supersymmetry and can be represented by quiver diagrams. The F and D term equations coincide with the ADHM construction. The Hilbert series of the moduli spaces of one instanton for classical gauge groups is easy to compute and turns out to take a particularly simple form which is previously unknown. This allows for a G invariant character expansion and hence easily generalisable for exceptional gauge groups, where an ADHM construction is not known. The conjectures for exceptional groups are further checked using some new techniques like sewing relations in Hilbert Series. This is applied to Argyres-Seiberg dualities. More... »

PAGES

100

References to SciGraph publications

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  • 2007-11-16. Counting BPS operators in gauge theories: quivers, syzygies and plethystics in JOURNAL OF HIGH ENERGY PHYSICS
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  • 2009-07-20. Six-dimensional DN theory and four-dimensional SO-USp quivers in JOURNAL OF HIGH ENERGY PHYSICS
  • 2004-05-11. A note on instanton counting for 𝒩 = 2 gauge theories with classical gauge groups in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-12-01. Argyres-Seiberg Duality and the Higgs Branch in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2007-12-06. Baryonic generating functions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-03-08. S-duality and 2d topological QFT in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-12-28. S-duality in N = 2 supersymmetric gauge theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-09-09. Webs of five-branes and 𝒩 = 2 superconformal field theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2008-09-22. Partition functions for membrane theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-03-20. Counting gauge invariants: the plethystic program in JOURNAL OF HIGH ENERGY PHYSICS
  • 2008-05-28. SQCD: a geometric aperçu in JOURNAL OF HIGH ENERGY PHYSICS
  • 2008-10-03. Counting gauge invariant operators in SQCD with classical gauge groups in JOURNAL OF HIGH ENERGY PHYSICS
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