Partition Functions of N=(2,2) Gauge Theories on S2 and Vortices View Full Text


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Article Info

DATE

2014-07-17

AUTHORS

Francesco Benini, Stefano Cremonesi

ABSTRACT

We apply localization techniques to compute the partition function of a two-dimensional N=(2,2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{N}=(2,2)}$$\end{document} R-symmetric theory of vector and chiral multiplets on S2. The path integral reduces to a sum over topological sectors of a matrix integral over the Cartan subalgebra of the gauge group. For gauge theories which would be completely Higgsed in the presence of a Fayet–Iliopoulos term in flat space, the path integral alternatively reduces to the product of a vortex times an antivortex partition functions, weighted by semiclassical factors and summed over isolated points on the Higgs branch. For applications, we evaluate the partition function for some U(N) gauge theories, showing equality of the path integrals for theories conjectured to be dual by Hori and Tong and deriving new expressions for vortex partition functions. More... »

PAGES

1483-1527

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    40 schema:description We apply localization techniques to compute the partition function of a two-dimensional N=(2,2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{N}=(2,2)}$$\end{document} R-symmetric theory of vector and chiral multiplets on S2. The path integral reduces to a sum over topological sectors of a matrix integral over the Cartan subalgebra of the gauge group. For gauge theories which would be completely Higgsed in the presence of a Fayet–Iliopoulos term in flat space, the path integral alternatively reduces to the product of a vortex times an antivortex partition functions, weighted by semiclassical factors and summed over isolated points on the Higgs branch. For applications, we evaluate the partition function for some U(N) gauge theories, showing equality of the path integrals for theories conjectured to be dual by Hori and Tong and deriving new expressions for vortex partition functions.
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    46 schema:keywords Cartan subalgebra
    47 Fayet-Iliopoulos term
    48 Higgs branch
    49 Hori
    50 S2
    51 Tong
    52 applications
    53 branches
    54 chiral multiplets
    55 equality
    56 expression
    57 factors
    58 flat space
    59 function
    60 gauge group
    61 gauge theory
    62 group
    63 integrals
    64 localization techniques
    65 matrix integrals
    66 multiplets
    67 new expression
    68 partition function
    69 path integral
    70 point
    71 presence
    72 products
    73 sector
    74 space
    75 subalgebra
    76 sum
    77 symmetric theory
    78 technique
    79 terms
    80 theory
    81 time
    82 topological sectors
    83 vector
    84 vortex partition function
    85 vortex time
    86 vortices
    87 schema:name Partition Functions of N=(2,2) Gauge Theories on S2 and Vortices
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