A matrix model for the latitude Wilson loop in ABJM theory

TL;DR

This paper introduces a matrix model for latitude Wilson loops in ABJM theory, connecting it to knot invariants, and provides exact results and strong coupling analysis, advancing understanding of Wilson loops and their dual string configurations.

Contribution

It proposes a novel matrix model for latitude Wilson loops in ABJM theory, linking it to torus knot invariants and enabling exact computations at weak and strong coupling.

Findings

Matrix model matches three-loop weak coupling calculations.

Fermi gas formulation allows systematic strong coupling expansion.

Results support string dual predictions for Wilson loops.

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 $B^{\theta}_{1/6}$ 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.