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

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

2011-12-19

arxiv.org/abs/1112.4524v1

Physics

High Energy Physics

High Energy Physics - Theory

34 pages, 9 figures

Scientific paper

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.

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