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

TL;DR

This paper investigates quantum corrections to 1/2 BPS Wilson loops in ${ m extbf{N}=4}$ super Chern-Simons-matter theories, confirming classical degeneracy at two loops and exploring potential quantum uplift at higher loops.

Contribution

It provides a two-loop analysis of Wilson loops, compares results with matrix model predictions, and discusses quantum effects on classical degeneracy and BPS properties.

Findings

Two-loop results show degeneracy persists for different Wilson loops.

Perturbative results match matrix model predictions after framing correction.

Potential three-loop effects could break classical degeneracy.

Abstract

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. Finally, we discuss the potential appearance of three-loop contributions that might break the classical degeneracy and briefly analyse possible implications on the BPS nature of these operators.