The Sudakov form factor to three loops in N=4 super Yang-Mills

TL;DR

This paper reviews the calculation of the three-loop Sudakov form factor in N=4 super Yang-Mills theory, highlighting its structure, transcendentality properties, and relation to QCD, with implications for understanding gauge theory amplitudes.

Contribution

It provides a detailed three-loop analysis of the Sudakov form factor in N=4 super Yang-Mills, including its scalar integral basis and transcendentality structure, extending previous lower-loop results.

Findings

Form factor expressed as scalar integrals with integer coefficients

Homogeneous transcendentality in expansion coefficients

Reproduction of cusp and collinear anomalous dimensions

Abstract

We review the results for the Sudakov form factor in N=4 super Yang-Mills theory up to the three-loop level. At each loop order, the form factor is expressed as a linear combination of only a handful scalar integrals, with small integer coefficients. Working in dimensional regularisation, the expansion coefficients of each integral exhibit homogeneous transcendentality in the Riemann zeta-function. We find that the logarithm of the form factor reproduces the correct values of the cusp and collinear anomalous dimensions. Moreover, the form factor in N=4 super Yang-Mills can be related to the leading transcendentality pieces of the QCD quark and gluon form factor. Finally, we comment briefly on the ultraviolet properties of the N=4 form factor in D>4 dimensions.