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Comments on knotted 1/2 BPS Wilson loops

In this paper, we show that the localization of three-dimensional N = 2 supersymmetric Chern-Simons theory on the ellipsoid-like squashed sphere is related to a nontrivial knot structure called torus knot. More precisely, we can capture the three sphere as the nontrivial so-called Seifert fibrations by regarding 1/2 BPS Wilson loops as U(1) fibers. The topology of knotted 1/2 BPS Wilson loops is controlled by squashing parameters. We calculate the 1/2 BPS condition of the Wilson loop and find perfect agreement with known results. We also remark on the level shift and framing anomaly.

preprint2013arXivOpen access
Akinori Tanaka
hep-th
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Akinori Tanaka

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