The quantum 1/2 BPS Wilson loop in ${\cal N}=4$ Chern-Simons-matter theories

Understand

In three dimensional ${\cal N}=4$ Chern-Simons-matter theories two independent fermionic Wilson loop operators can be defined, which preserve half of the supersymmetry charges and are cohomologically equivalent at classical level.

• We compute their three-loop expectation value in a convenient color sector and prove that the degeneracy is uplifted by quantum corrections.
• We expand the matrix model prediction in the same regime and by comparison we conclude that the quantum 1/2 BPS Wilson loop is the average of the two operators.
• We provide an all-loop argument to support this claim at any order.