The Principle of Maximal Transcendentality and the Four-Loop Collinear Anomalous Dimension

Abstract

We use the principle of maximal transcendentality and the universal nature of subleading infrared poles to extract the analytic value of the four-loop collinear anomalous dimension in planar ${\cal N}=4$ super-Yang-Mills theory from recent QCD results, obtaining $\hat{\cal G}_{0}^{(4)} = - 300 \zeta_7 - 256 \zeta_2 \zeta_5 - 384 \zeta_3 \zeta_4$. This value agrees with a previous numerical result to within 0.2 percent. It also provides the Regge trajectory, threshold soft anomalous dimension and rapidity anomalous dimension through four loops.