Construction and deconstruction of single instanton Hilbert series View Full Text


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Article Info

DATE

2015-12-17

AUTHORS

Amihay Hanany, Rudolph Kalveks

ABSTRACT

Many methods exist for the construction of the Hilbert series describing the moduli spaces of instantons. We explore some of the underlying group theoretic relationships between these various constructions, including those based on the Coulomb branches and Higgs branches of SUSY quiver gauge theories, as well as those based on generating functions derivable from the Weyl Character Formula. We show how the character description of the reduced single instanton moduli space (“RSIMS”) of any Classical or Exceptional group can be deconstructed faithfully in terms of characters or modified Hall-Littlewood polynomials of its regular semi-simple subgroups. We derive and utilise Highest Weight Generating (“HWG”) functions, both for the characters of Classical or Exceptional groups and for the Hall-Littlewood polynomials of unitary groups. We illustrate how the root space data encoded in extended Dynkin diagrams corresponds to relationships between the Coulomb branches of quiver gauge theories for RSIMS and those for T (SU(N )) moduli spaces. More... »

PAGES

1-83

References to SciGraph publications

  • 2004-09-17. ABCD of Instantons in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2007-11-16. Counting BPS operators in gauge theories: quivers, syzygies and plethystics in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-01-09. Hilbert series for moduli spaces of two instantons in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-01-03. Monopole operators and Hilbert series of Coulomb branches of 3d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} $\end{document} = 4 gauge theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2005-06-14. Instanton counting on blowup. I. 4-dimensional pure gauge theory in INVENTIONES MATHEMATICAE
  • 2014-12-16. Coulomb branch and the moduli space of instantons in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-07-13. Counting exceptional instantons in JOURNAL OF HIGH ENERGY PHYSICS
  • 2002-12-13. Monopole Operators and Mirror Symmetry in Three Dimensions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-01-18. Complete intersection moduli spaces in gauge theories in three dimensions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-06-28. The Hilbert series of the one instanton moduli space in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-11-07. Gauge Theories and Macdonald Polynomials in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2014-10-27. Highest weight generating functions for Hilbert series in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-03-15. The ABCDEFG of instantons and W-algebras in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-05-03. Supersymmetry enhancement by monopole operators in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-03-20. Counting gauge invariants: the plethystic program in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-09-30. Coulomb branch Hilbert series and Hall-Littlewood polynomials in JOURNAL OF HIGH ENERGY PHYSICS
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/jhep12(2015)118

    DOI

    http://dx.doi.org/10.1007/jhep12(2015)118

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1012023071


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