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Comments on knotted 1/2 BPS Wilson loops

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Abstract

In this paper, we show that the localization of three-dimensional \( \mathcal{N} = 2 \) 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.

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Authors and Affiliations

  1. Department of Physics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan

    Akinori Tanaka

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  1. Akinori Tanaka
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Correspondence to Akinori Tanaka.

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ArXiv ePrint: 1204.5975

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Tanaka, A. Comments on knotted 1/2 BPS Wilson loops. J. High Energ. Phys. 2012, 97 (2012). https://doi.org/10.1007/JHEP07(2012)097

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  • DOI: https://doi.org/10.1007/JHEP07(2012)097

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