Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data

TL;DR

This paper develops a non-perturbative framework for scattering amplitudes in N=4 Super-Yang-Mills theory using pentagon transitions, extending previous work to scalar excitations and validating predictions against perturbative data.

Contribution

It introduces an extended analysis of pentagon transitions including scalar excitations and provides a bootstrap method for finite coupling expressions, with validation against perturbative results.

Findings

Validated pentagon transition predictions up to three loops.

Extended the framework to include scalar excitations.

Provided explicit higher-loop predictions in notebooks.

Abstract

We elaborate on a non-perturbative formulation of scattering amplitudes/null polygonal Wilson loops in planar N=4 Super-Yang-Mills theory. The construction is based on a decomposition of the Wilson loop into elementary building blocks named pentagon transitions. Our discussion expands on a previous letter of the authors where these transitions were introduced and analyzed for the so-called gluonic excitations. In this paper we revisit these transitions and extend the analysis to the sector of scalar excitations. We restrict ourselves to the single particle transitions and bootstrap their finite coupling expressions using a set of axioms. Besides these considerations, the main focus of the paper is on the extraction of perturbative data from scattering amplitudes at weak coupling and its comparison against the proposed pentagon transitions. We present several tests for both the hexagon and heptagon (MHV and NMHV) amplitudes up to two- and three-loop orders. In attached notebooks we provide explicit higher-loop predictions obtained from our method.