ABJM Wilson loops in the Fermi gas approach

TL;DR

This paper reformulates the ABJM matrix model as a Fermi gas system, enabling exact calculations of Wilson loop vevs at all orders in 1/N and arbitrary coupling using WKB expansion, with explicit results involving Airy functions.

Contribution

It introduces a Fermi gas approach to compute ABJM Wilson loops at all orders, providing explicit formulas and connecting to previous low genus results.

Findings

Exact Wilson loop vevs expressed via Airy functions.

Calculations valid at all orders in 1/N and for any Chern-Simons coupling.

Reproduction of low genus results from 't Hooft expansion.

Abstract

The matrix model of ABJM theory can be formulated in terms of a Fermi gas in an external potential. We show that, in this formalism, vevs of Wilson loops correspond to averages of operators in the statistical-mechanical problem. This makes it possible to calculate these vevs at all orders in 1/N, up to exponentially small corrections, and for arbitrary Chern-Simons coupling, by using the WKB expansion. We present explicit results for the vevs of 1/6 and the 1/2 BPS Wilson loops, at any winding number, in terms of Airy functions. Our expressions are shown to reproduce the low genus results obtained previously in the 't Hooft expansion.