A matrix model for the latitude Wilson loop in ABJM theory

Abstract

In ABJ(M) theory, we propose a matrix model for the exact evaluation of BPS Wilson loops on a latitude circular contour, so providing a new weak-strong interpolation tool. Intriguingly, the matrix model turns out to be a particular case of that computing torus knot invariants in $U(N_1|N_2)$ Chern-Simons theory. At weak coupling we check our proposal against a three-loop computation, performed for generic framing, winding number and representation. The matrix model is amenable of a Fermi gas formulation, which we use to systematically compute the strong coupling and genus expansions. For the fermionic Wilson loop the leading planar behavior agrees with a previous string theory prediction. For the bosonic operator our result provides a clue for finding the corresponding string dual configuration. Our matrix model is consistent with recent proposals for computing Bremsstrahlung functions exactly in terms of latitude Wilson loops. As a by-product, we extend the conjecture for the exact $B_{1/6}^{\theta }$ Bremsstrahlung function to generic representations and test it with a four-loop perturbative computation. Finally, we propose an exact prediction for $B_{1/2}$ at unequal gauge group ranks.

73 pages; v2: several improvements, JHEP published version

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Cited by in corpus (11)

• Line defects and radiation in $\mathcal{N}=2$ theories
• Roadmap on Wilson loops in 3d Chern-Simons-matter theories
• Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT${}_1$
• Exact Bremsstrahlung functions in ABJM theory
• The Bremsstrahlung function of $\mathcal{N}=2$ SCQCD
• BPS Wilson loops and quiver varieties
• On three-point functions in ABJM and the latitude Wilson loop
• Wilson loop correlators in $\mathcal{N}=2$ superconformal quivers
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Supersymmetric Wilson loops in two dimensions and duality
• Interpolating Bremsstrahlung function in ABJM