Magnons and BFKL

Understand

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.