Antisymmetric Wilson loops in N = 4 SYM: from exact results to non-planar corrections

TL;DR

This paper derives the leading and sub-leading 1/N corrections for antisymmetric Wilson loops in N=4 SYM using exact localization results and a quantum system analogy, advancing understanding of non-planar effects.

Contribution

It introduces a method to extract 1/N corrections from exact localization results by relating Wilson loops to a truncated harmonic oscillator quantum system.

Findings

Explicit sum and integral formulas for 1/N corrections.

Connection between Wilson loops and a finite-dimensional quantum system.

Enhanced understanding of non-planar corrections in N=4 SYM.

Abstract

We consider the vacuum expectation values of 1/2-BPS circular Wilson loops in N=4 super Yang-Mills theory in the totally antisymmetric representation of the gauge group U(N) or SU(N). Localization and matrix model techniques provide exact, but rather formal, expressions for these expectation values. In this paper we show how to extract the leading and sub-leading behavior in a 1/N expansion with fixed 't Hooft coupling starting from these exact results. This is done by exploiting the relation between the generating function of antisymmetric Wilson loops and a finite-dimensional quantum system known as the truncated harmonic oscillator. Sum and integral representations for the 1/N terms are provided.