Space-time S-matrix and Flux-tube S-matrix at Finite Coupling

TL;DR

This paper introduces a non-perturbative framework for planar scattering amplitudes in N=4 SYM using a novel decomposition of Wilson loops into Pentagon transitions, connecting to the worldsheet S-matrix and applicable at any coupling.

Contribution

It presents a new non-perturbative formulation based on Pentagon transitions that relate to the worldsheet S-matrix, enabling bootstrap at any coupling and matching known weak and strong coupling results.

Findings

Successfully matches weak coupling data.

Reproduces strong coupling Y-system.

Provides a subsector solution called the gluonic part.

Abstract

We propose a non-perturbative formulation of planar scattering amplitudes in N=4 SYM or, equivalently, polygonal Wilson loops. The construction is based on the OPE approach and introduces a new decomposition of the Wilson loop in terms of fundamental building blocks named Pentagon transitions. These transitions satisfy a simple relation to the worldsheet S-matrix on top of the so called Gubser-Klebanov-Polyakov vacuum which allows us to bootstrap them at any value of the coupling. In this letter we present a subsector of the full solution to scattering amplitudes which we call the gluonic part. We match our results with both weak and strong coupling data available in the literature. For example, the strong coupling Y-system can be understood in this approach.