Comments on knotted 1/2 BPS Wilson loops

Understand

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.