Planar scattering amplitudes from Wilson loops

TL;DR

This paper derives a new expression linking planar gauge theory scattering amplitudes to sums of Wilson loops, revealing dualities and proposing a conjecture connecting position and momentum Wilson loops in N=4 SYM.

Contribution

It introduces a novel formulation of scattering amplitudes using Wilson loops, incorporating T-duality and holographic principles, advancing the understanding of gauge/string duality.

Findings

Expression for amplitudes as sums of Wilson loops

Connection between T-duality and Fourier transform in loop space

Conjecture relating position and momentum Wilson loops in N=4 SYM

Abstract

We derive an expression for parton scattering amplitudes of planar gauge theory in terms of sums of Wilson loops. We study in detail the example of Yang-Mills theory with an adjoint Higgs field. The expression exhibits the T-duality performed by Alday and Maldacena in the AdS dual as a Fourier transform in loop space. When combined with the AdS/CFT correspondence for Wilson loops and a strong coupling argument for the dominance of 1PI diagrams, this leads to a derivation of the Alday-Maldacena holographic prescription for scattering amplitudes in terms of momentum Wilson loops. The formula leads to a conjecture for a relationship between position-space and momentum-space Wilson loops in N=4 SYM at finite coupling.