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

TL;DR

This work provides a non-perturbative, integrability-based framework to compute scattering amplitudes in planar ${ m N}=4$ SYM via the flux-tube S-matrix and pentagon transitions, extending the pentagon bootstrap from gluons to scalars. By bootstrapping single-particle transitions at finite coupling and matching them to weak-coupling perturbative data from hexagon and heptagon amplitudes, the authors derive explicit scalar and gluon transition and measure formulas, including NMHV components, with consistent OPE and crossing structures. The approach yields concrete predictions up to three loops for several configurations and supplies accompanying notebooks for higher-loop checks, strengthening the link between 2D flux-tube dynamics and 4D amplitudes. The results illuminate how integrability, OPE, and Wilson-loop data constrain the full amplitude structure and suggest avenues toward strong-coupling re-summations and broader fermionic/bound-state extensions.

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.