Hexagon OPE Resummation and Multi-Regge Kinematics

Understand

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.