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

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.