We construct the three-loop four-point amplitude of N=8 supergravity using the unitarity method. The amplitude is ultraviolet finite in four dimensions. Novel cancellations, not predicted by traditional superspace power-counting arguments, render its degree of divergence in D dimensions to be no worse than that of N=4 super-Yang-Mills theory -- a finite theory in four dimensions. Similar cancellations can be identified at all loop orders in certain unitarity cuts, suggesting that N=8 supergravity may be a perturbatively finite theory of quantum gravity.
@article{arxiv.hep-th/0702112,
title = {Three-Loop Superfiniteness of N=8 Supergravity},
author = {Z. Bern and J. J. Carrasco and L. J. Dixon and H. Johansson and D. A. Kosower and R. Roiban},
journal= {arXiv preprint arXiv:hep-th/0702112},
year = {2008}
}
Comments
5 pages, 4 figures. In v2 references and minor clarifications added