Magnons and BFKL

TL;DR

This paper derives the magnon dispersion relation in planar N=4 supersymmetric Yang-Mills theory from double logarithmic contributions to anomalous dimensions, connecting spin chain magnons with BFKL eigenfunctions.

Contribution

It provides the first all-loop expression for the magnon dispersion relation based on double logarithmic resummation and explores its relation to BFKL eigenfunctions.

Findings

Derived the magnon dispersion relation from three-loop anomalous dimensions.

Established agreement with known expansions for spin-one and double logarithmic BFKL contributions.

Proposed a potential mapping between spin chain magnons and BFKL eigenfunctions.

Abstract

We extract from the double logarithmic contributions to DGLAP anomalous dimensions for twist-two operators up to three-loops the magnon dispersion relation for planar N=4 supersymmetric Yang-Mills. Perturbatively the magnon dispersion relation agrees with the expansion of the anomalous dimension for spin-one as well as with the non-collinear double logarithmic contributions to the BFKL anomalous dimensions analytically extended to negative spin. The all-loop expression for the magnon dispersion relation is determined by the double logarithmic resummation of the corresponding Bethe-Salpeter equation. A potential map relating the spin chain magnon to BFKL eigenfunctions in the double logarithm approximation is suggested.