Comments on knotted 1/2 BPS Wilson loops

Abstract

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.

13 pages, 8 figures, typos corrected

References in corpus (5)

• SUSY Gauge Theories on Squashed Three-Spheres
• Notes on SUSY Gauge Theories on Three-Sphere
• Cohomological localization of Chern-Simons theory
• AGT on the S-duality Wall
• Observables and Correlators in Nonrelativistic ABJM Theory

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