The Ultraviolet Behavior of N=8 Supergravity at Four Loops

Abstract

We describe the construction of the complete four-loop four-particle amplitude of N=8 supergravity. The amplitude is ultraviolet finite, not only in four dimensions, but in five dimensions as well. The observed extra cancellations provide additional non-trivial evidence that N=8 supergravity in four dimensions may be ultraviolet finite to all orders of perturbation theory.

5 pages, 4 figures. v2 contains minor corrections, including flipping sign of eq. (1). Complete results, including mathematica readable form, presented in the directory aux/ included in the source of this manuscript. As certain computer operating systems (e.g. Windows) preclude the naming of directories "aux" we also host this data at: http://www.physics.ucla.edu/~jjmc/auxiliaryData.tgz