The full four-loop cusp anomalous dimension in N = 4 super Yang-Mills and QCD

• Published in: The journal of high energy physics Vol. 2020; no. 4
• Main Authors: Henn, Johannes M., Korchemsky, Gregory P., Mistlberger, Bernhard
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 03.04.2020; Springer Nature B.V
• Subjects: Classical and Quantum Gravitation; Cusps; Elementary Particles; High energy physics; Insertion; Physics; Physics and Astronomy; Quantum chromodynamics; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Supersymmetry; Yang-Mills theory; Scattering Amplitudes; Resummation; 1/N Expansion; Perturbative QCD
• ISSN: 1029-8479
• DOI: 10.1007/JHEP04(2020)018

A bstract We present the complete formula for the cusp anomalous dimension at four loops in QCD and in maximally supersymmetric Yang-Mills. In the latter theory it is given by Γ cusp , A α s 4 = − α s N π 4 73 π 6 20160 + ζ 3 2 8 + 1 N 2 31 π 6 5040 + 9 ζ 3 2 4 . Our approach is based on computing the correlation function of a rectangular light-like Wilson loop with a Lagrangian insertion, normalized by the expectation value of the Wilson loop. In maximally supersymmetric Yang-Mills theory, this ratio is a finite function of a cross-ratio and the coupling constant. We compute it to three loops, including the full colour dependence. Integrating over the position of the Lagrangian insertion gives the four-loop Wilson loop. We extract its leading divergence, which determines the four-loop cusp anomalous dimension. Finally, we employ a supersymmetric decomposition to derive the last missing ingredient in the corresponding QCD result.