irregular states and isolated superconformal field theories View Full Text


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Article Info

DATE

2013-03-27

AUTHORS

Hiroaki Kanno, Kazunobu Maruyoshi, Shotaro Shiba, Masato Taki

ABSTRACT

We explore the proposal that the six-dimensional (2, 0) theory on the Riemann surface with irregular punctures leads to a four-dimensional gauge theory coupled to the isolated \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 $\end{document} superconformal theories of Argyres-Douglas type, and to two-dimensional conformal field theory with irregular states. Following the approach of Gaiotto-Teschner for the Virasoro case, we construct \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{\mathcal{W}}_3} $\end{document} irregular states by colliding a single SU(3) puncture with several regular punctures of simple type. If n simple punctures are colliding with the SU(3) puncture, the resulting irregular state is a simultaneous eigenvector of the positive modes Ln, . . . , L2n and W2n, . . . , W3n of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{\mathcal{W}}_3} $\end{document} algebra. We find the corresponding isolated SCFT with an SU(3) flavor symmetry as a nontrivial IR fixed point on the Coulomb branch of the SU(3) linear quiver gauge theories, by confirming that its Seiberg-Witten curve correctly predicts the conditions for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{\mathcal{W}}_3} $\end{document} irregular states. We also compare these SCFT’s with the ones obtained from the BPS quiver method. More... »

PAGES

147

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    31 schema:description We explore the proposal that the six-dimensional (2, 0) theory on the Riemann surface with irregular punctures leads to a four-dimensional gauge theory coupled to the isolated \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 $\end{document} superconformal theories of Argyres-Douglas type, and to two-dimensional conformal field theory with irregular states. Following the approach of Gaiotto-Teschner for the Virasoro case, we construct \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{\mathcal{W}}_3} $\end{document} irregular states by colliding a single SU(3) puncture with several regular punctures of simple type. If n simple punctures are colliding with the SU(3) puncture, the resulting irregular state is a simultaneous eigenvector of the positive modes Ln, . . . , L2n and W2n, . . . , W3n of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{\mathcal{W}}_3} $\end{document} algebra. We find the corresponding isolated SCFT with an SU(3) flavor symmetry as a nontrivial IR fixed point on the Coulomb branch of the SU(3) linear quiver gauge theories, by confirming that its Seiberg-Witten curve correctly predicts the conditions for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{\mathcal{W}}_3} $\end{document} irregular states. We also compare these SCFT’s with the ones obtained from the BPS quiver method.
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    38 schema:keywords Coulomb branch
    39 IR
    40 L2N
    41 Ln
    42 Riemann surface
    43 SCFTs
    44 Seiberg-Witten curve
    45 Virasoro case
    46 W2N
    47 algebra
    48 approach
    49 branches
    50 cases
    51 conditions
    52 conformal field theory
    53 corresponding
    54 curves
    55 eigenvectors
    56 field theory
    57 flavor symmetry
    58 four-dimensional gauge theories
    59 gauge theory
    60 irregular punctures
    61 irregular state
    62 method
    63 nontrivial IR
    64 one
    65 point
    66 proposal
    67 puncture
    68 quiver gauge theories
    69 regular punctures
    70 simple puncture
    71 simple type
    72 simultaneous eigenvectors
    73 six-dimensional theory
    74 state
    75 superconformal field theories
    76 superconformal theories
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