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 useful for resolving the general ultraviolet behavior of supergravity theories.
@article{arxiv.1207.6666,
title = {The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory},
author = {Z. Bern and J. J. M. Carrasco and H. Johansson and R. Roiban},
journal= {arXiv preprint arXiv:1207.6666},
year = {2015}
}
Comments
5 pages, 4 figures, RevTex. Ancillary file included. v2 minor corrections, corrected references and overall phase in eq. (5), matching journal version