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

The Ultraviolet Behavior of N=8 Supergravity at Four Loops