The three-loop form factor in N=4 super Yang-Mills

TL;DR

This paper computes the three-loop Sudakov form factor in N=4 super Yang-Mills theory, demonstrating uniform transcendentality, infrared divergence exponentiation, and unexpected ultraviolet cancellations, with implications for QCD and higher-dimensional theories.

Contribution

It presents the first three-loop calculation of the form factor in N=4 SYM with uniform transcendentality and reveals novel ultraviolet cancellation phenomena.

Findings

Verified infrared divergence exponentiation at three loops.

Established relation to leading transcendentality parts of QCD form factors.

Discovered unexpected ultraviolet cancellations in higher dimensions.

Abstract

In this paper we study the Sudakov form factor in N=4 super Yang-Mills theory to the three-loop order. The latter is expressed in terms of planar and non-planar loop integrals. We show that it is possible to choose a representation in which each loop integral has uniform transcendentality. We verify analytically the expected exponentiation of the infrared divergences with the correct values of the three-loop cusp and collinear anomalous dimensions in dimensional regularisation. We find that the form factor in N=4 super Yang-Mills can be related to the leading transcendentality part of the quark and gluon form factors in QCD. We also study the ultraviolet properties of the form factor in D>4 dimensions, and find unexpected cancellations, resulting in an improved ultraviolet behaviour.