The four-loop cusp anomalous dimension in N = 4 super Yang-Mills and analytic integration techniques for Wilson line integrals

• Published in: The journal of high energy physics Vol. 2013; no. 9; p. 1
• Main Authors: Henn, Johannes M, Huber, Tobias
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 26.09.2013
• Subjects: High energy physics
• ISSN: 1029-8479
• DOI: 10.1007/JHEP09(2013)147

Abstract Correlation functions of Wilson lines are relevant for describing the infrared structure of scattering amplitudes. We develop a new method for evaluating a wide class of such Wilson line integrals, and apply it to the calculation of the velocity-dependent cusp anomalous dimension in maximally supersymmetric Yang-Mills theory. We compute the four-loop non-planar correction in a recently introduced scaling limit. Moreover, we derive the full planar four-loop result by means of an ansatz which is based on the structure of known analytic results. We determine the coefficients in this ansatz by making use of a relationship to massive scattering amplitudes. As a corollary, our analytical result confirms the four-loop value of the light-like cusp anomalous dimension. Finally, we use the available perturbative data, as well as insight from AdS/CFT, in order to extrapolate the leading order values at strong coupling. The latter agree within two per cent with the corresponding string theory result, over a wide range of parameters.