Coulomb branch Hilbert series and three dimensional Sicilian theories View Full Text


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Article Info

DATE

2014-09-30

AUTHORS

Stefano Cremonesi, Amihay Hanany, Noppadol Mekareeya, Alberto Zaffaroni

ABSTRACT

We evaluate the Coulomb branch Hilbert series of mirrors of three dimensional Sicilian theories, which arise from compactifying the 6d (2, 0) theory with symmetry G on a circle times a Riemann surface with punctures. We obtain our result by gluing together the Hilbert series for building blocks Tρ(G), where ρ is a certain partition related to the dual group of G, which we evaluated in a previous paper. The result is expressed in terms of a class of symmetric functions, the Hall-Littlewood polynomials. As expected from mirror symmetry, our results agree at genus zero with the superconformal index prediction for the Higgs branch Hilbert series of the Sicilian theories and extend it to higher genus. In the A1 case at genus zero, we also evaluate the Coulomb branch Hilbert series of the Sicilian theory itself, showing that it only depends on the number of external legs. More... »

PAGES

185

References to SciGraph publications

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  • 2002-12-13. Monopole Operators and Mirror Symmetry in Three Dimensions in JOURNAL OF HIGH ENERGY PHYSICS
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  • 2011-08-01. 3d partition function as overlap of wavefunctions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-06-06. Superconformal indices of three-dimensional theories related by mirror symmetry in JOURNAL OF HIGH ENERGY PHYSICS
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  • 2000-11-22. Mirror symmetry by O3-planes in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-01-21. Sicilian gauge theories and \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} = 1 dualities in JOURNAL OF HIGH ENERGY PHYSICS
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