Exact results for Wilson loops in superconformal Chern-Simons theories with matter

A Kapustin, B Willett, I Yaakov - Journal of High Energy Physics, 2010 - Springer
A Kapustin, B Willett, I Yaakov
Journal of High Energy Physics, 2010Springer
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\(\mathcal {N}= 2\) 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 …
Abstract
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 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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