Wilson loops in ABJM theory reloaded

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.