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We review the results for the Sudakov form factor in N=4 super Yang-Millstheory up to the three-loop level. At each loop order, the form factor isexpressed as a linear combination of only a handful scalar integrals, withsmall integer coefficients. Working in dimensional regularisation, theexpansion coefficients of each integral exhibit homogeneous transcendentalityin the Riemann zeta-function. We find that the logarithm of the form factorreproduces 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 leadingtranscendentality pieces of the QCD quark and gluon form factor. Finally, wecomment briefly on the ultraviolet properties of the N=4 form factor in D>4dimensions.

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