Probing Wilson loops in ${\cal N}=4$ Chern-Simons-matter theories at weak coupling

Understand

For three-dimensional ${\cal N}=4$ super Chern-Simons-matter theories associated to necklace quivers $U(N_0) \times U(N_1) \times \cdots U(N_{2r-1}) $, we study at quantum level the two kinds of 1/2 BPS Wilson loop operators recently introduced in arXiv:1506.07614.

• We perform a two-loop evaluation and find the same result for the two kinds of operators, so moving to higher loops a possible quantum uplift of the classical degeneracy.
• We also compute the 1/4 BPS bosonic Wilson loop and discuss the quantum version of the cohomological equivalence between fermionic and bosonic Wilson loops.
• We compare the perturbative result with the Matrix Model prediction and find perfect matching, after identification and remotion of a suitable framing factor.