Hexagon OPE Resummation and Multi-Regge Kinematics

TL;DR

The paper develops a systematic OPE-based resummation for the hexagon Wilson loop in planar N=4 SYM, focusing on a double-scaling limit where gluon bound states dominate. By resumming single-particle gluon bound states into two-variable polylogarithms and analyzing their MRK behavior after analytic continuation, the authors show that MRK is governed by these states up to five loops and that the full MRK remainder function can be reconstructed using single-valuedness. They demonstrate consistency with the hexagon-function bootstrap, relate the double-scaling results to M_{0,5} polylogarithms, and verify agreement with the BFKL description up to five loops. The work highlights the power of single-valued polylogarithms in capturing high-energy scattering in N=4 SYM and provides a concrete path to obtaining MRK amplitudes from collinear OPE data.

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.

Figures (3)

• Figure 1: Decomposition of the light-like hexagonal Wilson loop in to a top pentagon, bottom pentagon and intermediate square. The collinear limit is indicated by the arrows, and each term in the expansion around it may be mapped to an excitation of an integrable colour-electric flux tube, sourced by the two sides of $W_\Box$ adjacent to the ones becoming collinear.
• Figure 2: Log-linear plot of the imaginary part of the 5-loop hexagon remainder function in multi-Regge kinematics at $(\text{Next-to})^3$-Leading Logarithmic approximation, $g^{(5)}_1$, on the line $w=w^\star$.
• Figure 3: Imaginary part $g^{(5)}_0$ of the 5-loop hexagon remainder function in multi-Regge kinematics at $(\text{Next-to})^4$-Leading Logarithmic approximation on the line $w=w^\star$.