Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction

TL;DR

This paper extends the duality between scattering amplitudes and Wilson loops in ${ m f N}=4$ SYM to include the first non-planar correction, providing new tools for understanding non-planar contributions.

Contribution

It introduces a duality between double trace amplitudes and correlation functions of null Wilson lines, extending the planar duality to non-planar corrections.

Findings

Duality tested at one-loop order.

Dual string in AdS confirms the duality.

Loop integrand extended beyond planar limit.

Abstract

We study the first non-planar correction to gluon scattering amplitudes in ${\cal N}=4$ SYM theory. The correction takes the form of a double trace partial amplitude and is suppressed by one power of $1/N$ with respect to the leading single trace contribution. We extend the duality between planar scattering amplitudes and null polygonal Wilson loops to the double trace amplitude. The new duality relates the amplitude to the correlation function of two infinite null polygonal Wilson lines that are subject to a quantum periodicity constraint. We test the duality perturbatively at one-loop order and demonstrate it for the dual string in AdS. The duality allows us to extend the notion of the loop integrand beyond the planar limit and to determine it using recursion relations. It also allows one to apply the integrability-based pentagon operator product expansion approach to the first non-planar order.