Higgs branch localization in three dimensions View Full Text


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Article Info

DATE

2014-05-08

AUTHORS

Francesco Benini, Wolfger Peelaers

ABSTRACT

We show that the supersymmetric partition function of 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} =2 R-symmetric Chern-Simons-matter theories on the squashed S3 and on S2× S1 can be computed with the so-called Higgs branch localization method, alternative to the more standard Coulomb branch localization. For theories that could be completely Higgsed by Fayet-Iliopoulos terms, the path integral is dominated by BPS vortex strings sitting at two circles in the geometry. In this way, the partition function directly takes the form of a sum, over a finite number of points on the classical Coulomb branch, of a vortex-string times an antivortex-string partition functions. More... »

PAGES

30

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    41 schema:description We show that the supersymmetric partition function of 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} =2 R-symmetric Chern-Simons-matter theories on the squashed S3 and on S2× S1 can be computed with the so-called Higgs branch localization method, alternative to the more standard Coulomb branch localization. For theories that could be completely Higgsed by Fayet-Iliopoulos terms, the path integral is dominated by BPS vortex strings sitting at two circles in the geometry. In this way, the partition function directly takes the form of a sum, over a finite number of points on the classical Coulomb branch, of a vortex-string times an antivortex-string partition functions.
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    48 Coulomb branch
    49 Fayet-Iliopoulos term
    50 Higgs branch localization
    51 S1
    52 S3
    53 alternative
    54 branches
    55 circle
    56 dimensions
    57 finite number
    58 form
    59 function
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    61 integrals
    62 localization
    63 localization method
    64 matter theory
    65 method
    66 number
    67 partition function
    68 path integral
    69 point
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    71 string
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