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

Abstract

In three dimensional $\mathcal{N}=4$ 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. As a by-product, we identify the localization result at three loops as a correction to the framing factor induced by matter interactions. Finally, we comment on the quantum properties of the non-1/2 BPS Wilson loop operator defined as the difference of the two fermionic ones.

arXiv comment22 pages + appendixes, 4 figures, 1 Table

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• Notes on hyperloops in N=4 Chern-Simons-matter theories
• A matrix model for the latitude Wilson loop in ABJM theory
• BPS Wilson loops and quiver varieties
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• Two-Point Functions in ABJM Matrix Model
• Conformal and non-conformal hyperloop deformations of the 1/2 BPS circle
• Loop Operators in Three-Dimensional $\mathcal{N}=2$ Fishnet Theories
• Bootstrap of the defect 1/2 BPS Wilson lines in N=4 Chern-Simons-matter theories
• A network of hyperloops