Hexagon OPE resummation and multi-Regge kinematics

We analyse the ope contribution of gluon bound states in the double scaling limit of the hexagonal wilson loop in planar $$ mathcal{n}=4 $$ 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 → 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.