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arxiv: 0909.4559 · v4 · submitted 2009-09-24 · ✦ hep-th

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Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter

Anton Kapustin , Brian Willett , Itamar Yaakov
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classification ✦ hep-th
keywords theorieschern-simonsloopsresultswilsonagreementlocalizationmatter
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We use localization techniques to compute the expectation values of supersymmetric Wilson loops in Chern-Simons theories with matter. We find the path-integral reduces to a non-Gaussian matrix model. The Wilson loops we consider preserve a single complex supersymmetry, and exist in any N=2 theory, though the localization requires superconformal symmetry. We present explicit results for the cases of pure Chern-Simons theory with gauge group U(N), showing agreement with the known results, and ABJM, showing agreement with perturbative calculations. Our method applies to other theories, such as Gaiotto-Witten theories, BLG, and their variants.

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