Hexagon OPE Resummation and Multi-Regge Kinematics

TL;DR

This paper develops a systematic method to resum gluon bound state contributions in the hexagon Wilson loop of planar N=4 super Yang-Mills theory, enabling reconstruction of the six-gluon scattering amplitude in multi-Regge kinematics up to five loops.

Contribution

It introduces a perturbative resummation technique for gluon bound states and demonstrates that only single-particle states contribute in the multi-Regge limit, facilitating high-loop calculations.

Findings

Resummation expressed in two-variable polylogarithms.

Single-particle gluon bound states dominate in the multi-Regge limit.

Full six-gluon amplitude reconstructed up to five loops.

Abstract

We analyse the OPE contribution of gluon bound states in the double scaling limit of the hexagonal Wilson loop in planar N=4 super Yang-Mills theory. We provide a systematic procedure for perturbatively resumming the contributions from single-particle bound states of gluons and expressing the result order by order in terms of two-variable polylogarithms. We also analyse certain contributions from two-particle gluon bound states and find that, after analytic continuation to the $2\to 4$ Mandelstam region and passing to multi-Regge kinematics (MRK), only the single-particle gluon bound states contribute. From this double-scaled version of MRK we are able to reconstruct the full hexagon remainder function in MRK up to five loops by invoking single-valuedness of the results.