Systematics of the cusp anomalous dimension

TL;DR

This paper analyzes the velocity-dependent cusp anomalous dimension in supersymmetric Yang-Mills theory, providing a perturbative solution method, exploring special properties of the results, and comparing strong coupling limits with string theory predictions.

Contribution

It introduces a systematic perturbative approach to solve the Schrodinger problem for the cusp anomalous dimension and uncovers special properties of the harmonic polylogarithm structure.

Findings

Solution expressed in harmonic polylogarithms up to six loops

Only single zeta values appear in the light-like limit

Agreement with string theory at strong coupling

Abstract

We study the velocity-dependent cusp anomalous dimension in supersymmetric Yang-Mills theory. In a paper by Correa, Maldacena, Sever, and one of the present authors, a scaling limit was identified in which the ladder diagrams are dominant and are mapped onto a Schrodinger problem. We show how to solve the latter in perturbation theory and provide an algorithm to compute the solution at any loop order. The answer is written in terms of harmonic polylogarithms. Moreover, we give evidence for two curious properties of the result. Firstly, we observe that the result can be written using a subset of harmonic polylogarithms only, at least up to six loops. Secondly, we show that in a light-like limit, only single zeta values appear in the asymptotic expansion, again up to six loops. We then extend the analysis of the scaling limit to systematically include subleading terms. This leads to a Schrodinger-type equation, but with an inhomogeneous term. We show how its solution can be computed in perturbation theory, in a way similar to the leading order case. Finally, we analyze the strong coupling limit of these subleading contributions and compare them to the string theory answer. We find agreement between the two calculations.