Coulomb branch Hilbert series and Hall-Littlewood polynomials View Full Text


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Article Info

DATE

2014-09

AUTHORS

Stefano Cremonesi, Amihay Hanany, Noppadol Mekareeya, Alberto Zaffaroni

ABSTRACT

There has been a recent progress in understanding the chiral ring of 3d N = 4 superconformal gauge theories by explicitly constructing an exact generating function (Hilbert series) counting BPS operators on the Coulomb branch. In this paper we introduce Coulomb branch Hilbert series in the presence of background magnetic charges for flavor symmetries, which are useful for computing the Hilbert series of more general theories through gluing techniques. We find a simple formula of the Hilbert series with background magnetic charges for Tρ(G) theories in terms of Hall-Littlewood polynomials. Here G is a classical group and ρ is a certain partition related to the dual group of G. The Hilbert series for vanishing background magnetic charges show that Coulomb branches of Tρ(G) theories are complete intersections. We also demonstrate that mirror symmetry maps background magnetic charges to baryonic charges. More... »

PAGES

178

References to SciGraph publications

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  • 2007-12-06. Baryonic generating functions in JOURNAL OF HIGH ENERGY PHYSICS
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  • 2013-01. Hilbert series for moduli spaces of two instantons in JOURNAL OF HIGH ENERGY PHYSICS
  • 2014-01. 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
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  • 2000-11-22. Mirror symmetry by O3-planes in JOURNAL OF HIGH ENERGY PHYSICS
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  • 2011-06. Superconformal indices of three-dimensional theories related by mirror symmetry in JOURNAL OF HIGH ENERGY PHYSICS
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