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} ... View Full Text


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Article Info

DATE

2014-01-03

AUTHORS

Stefano Cremonesi, Amihay Hanany, Alberto Zaffaroni

ABSTRACT

This paper addresses a long standing problem - to identify the chiral ring and moduli space (i.e. as an algebraic variety) on the Coulomb branch of an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} $\end{document} = 4 superconformal field theory in 2+1 dimensions. Previous techniques involved a computation of the metric on the moduli space and/or mirror symmetry. These methods are limited to sufficiently small moduli spaces, with enough symmetry, or to Higgs branches of sufficiently small gauge theories. We introduce a simple formula for the Hilbert series of the Coulomb branch, which applies to any good or ugly three-dimensional \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} $\end{document} = 4 gauge theory. The formula counts monopole operators which are dressed by classical operators, the Casimir invariants of the residual gauge group that is left unbroken by the magnetic flux. We apply our formula to several classes of gauge theories. Along the way we make various tests of mirror symmetry, successfully comparing the Hilbert series of the Coulomb branch with the Hilbert series of the Higgs branch of the mirror theory. More... »

PAGES

5

References to SciGraph publications

  • 2011-05-03. Supersymmetry enhancement by monopole operators in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-11-16. Counting BPS operators in gauge theories: quivers, syzygies and plethystics in JOURNAL OF HIGH ENERGY PHYSICS
  • 2004-03-03. Monopole operators in three-dimensional š¯’© = 4 SYM and mirror symmetry in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-01-26. Charges of monopole operators in Chern-Simons Yang-Mills theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 1999-04-23. On mirror symmetry in three dimensional Abelian gauge theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 1998-04-03. Instanton effects in three-dimensional supersymmetric gauge theories with matter in JOURNAL OF HIGH ENERGY PHYSICS
  • 2013-11-26. Redeeming bad theories 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
  • 2000-06-28. (Anti-)Instantons and the Atiyah-Hitchin manifold in JOURNAL OF HIGH ENERGY PHYSICS
  • 2000-06-07. On orientifolds, discrete torsion, branes and M theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2002-11-26. Topological Disorder Operators in Three-Dimensional Conformal Field Theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2000-07-11. Dynamics of š¯’© = 2 supersymmetric Chern-Simons theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2000-11-22. Mirror symmetry by O3-planes in JOURNAL OF HIGH ENERGY PHYSICS
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    DOI

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    DIMENSIONS

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