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.
Highlights
We find that only a particular subset of these functions arises, which is consistent with the functions having restricted branch cuts, and with the idea that they are particular limits of hexagon functions [16, 17] describing the full six-point remainder function
From the knowledge of the single-particle bound state contributions to the double scaling limit we can produce all but the power-suppressed terms of the MHV hexagon in multi-Regge kinematics corresponding to high energy gluon scattering in the 2 → 4 Mandelstam region
We describe in 2.4 why the class of functions so obtained is consistent with the idea that the full hexagonal Wilson loop remainder function is expressed in terms of hexagon functions
Summary
An operator product expansion (OPE) for light-like Wilson loops was introduced in [23] and refined in many papers [24,25,26,27, 29, 41,42,43,44,45] It describes the near-collinear regime of a particular ratio of light-like Wilson loops, denoted by W. These excitations propagate to the top part of the Wilson loop where they are absorbed Both the spectrum of excitations [28], which controls the propagation of states, and overlap functions [25], describing their production and absorption, can be studied at finite ’t Hooft coupling using integrability. We will describe the ‘double-scaling’ limit of W (and the remainder function R6) which allows us to consider contributions to the sum over states (2.5) coming from gluons only
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