Ultraviolet Behavior ofN 1⁄4 8 Supergravity at Four Loops

Z. Bern, J. J.M. Carrasco, L. J. Dixon, H. Johansson, and R. Roiban Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1547, USA SLAC National Accelerator Laboratory, Stanford University, Stanford, California 94309, USA Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA (Received 25 May 2009; published 17 August 2009) We describe the construction of the complete four-loop four-particle amplitude ofN 1⁄4 8 supergravity. The amplitude is ultraviolet finite, not only in four dimensions, but in five dimensions as well. The observed extra cancellations provide additional nontrivial evidence that N 1⁄4 8 supergravity in four dimensions may be ultraviolet finite to all orders of perturbation theory.