Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion

TL;DR

This paper develops all-loop formulas for flux-tube gluonic transitions in N=4 SYM, enabling precise computation of scattering amplitudes that match perturbative results up to four loops.

Contribution

It introduces a unified framework for all-loop flux-tube gluonic transitions using factorization and fusion, extending previous conjectures to arbitrary excitations.

Findings

Derived all-loop expressions for flux-tube gluonic transitions.

Achieved perfect agreement with perturbative data up to four loops.

Enabled computation of MHV and NMHV amplitudes at any loop order.

Abstract

We analyze the pentagon transitions involving arbitrarily many flux-tube gluonic excitations and bound states thereof in planar N=4 Super-Yang-Mills theory. We derive all-loop expressions for all these transitions by factorization and fusion of the elementary transitions for the lightest gluonic excitations conjectured in a previous paper. We apply the proposals so obtained to the computation of MHV and NMHV scattering amplitudes at any loop order and find perfect agreement with available perturbative data up to four loops.