Z. Bern, J. J. M. Carrasco, H. Johansson, R. Roiban
Using the method of maximal cuts, we construct the complete D-dimensional integrand of the five-loop four-point amplitude of N = 4 super-Yang-Mills theory, including nonplanar contributions. In the critical dimension where this amplitude becomes ultraviolet divergent, we present a compact explicit expression for the nonvanishing ultraviolet divergence in terms of three vacuum integrals. This construction provides a crucial step towards obtaining the corresponding amplitude of N = 8 supergravity required to resolve the general ultraviolet behavior of supergravity theories.
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http://arxiv.org/abs/1207.6666
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