Wilson loops in ABJM theory reloaded

TL;DR

This paper introduces a new method using supersymmetric localization and the Fermi gas formalism to compute Wilson loops in ABJM theory exactly for any gauge group rank and Chern-Simons level, resolving previous discrepancies.

Contribution

It develops an operator-based approach within the Fermi gas formalism to derive exact Wilson loop expressions in ABJM theory, connecting them to the partition function and resolving longstanding issues.

Findings

Exact formulas for Wilson loops in ABJM theory derived

Reproduces weak-coupling expansion at large k

Matches high-precision numerical results at large N

Abstract

We present a new technique for computing supersymmetric Wilson loops in the ABJM theory via supersymmetric localization, valid for arbitrary values of the rank of the gauge group $N$ and the Chern-Simons level $k$. The approach relies on an operator representation of the Wilson loops within the Fermi gas formalism in terms of the resolvent of a certain integral operator previously encountered in the computation of the ABJM partition function on the round three-sphere. By deriving a set of nontrivial relations for this resolvent, we obtain exact expressions for the generating functions of Wilson loops in terms of the partition function. For large $k$, these expressions reproduce the weak-coupling expansion of the Wilson loops, and in the large-$N$ limit at fixed $k$ they match previously obtained high-precision numerical results. This analysis also resolves the longstanding discrepancy between numerical data and the semiclassical expression for the $1/6$ BPS Wilson loop.