Two-loop graviton scattering relation and IR behavior in N=8N=8 supergravity

We derive an ABDK-like relation between the one- and two-loop four-graviton amplitudes in N=8N=8 supergravity. Specifically we show that the infrared-divergent part of the two-loop amplitude is one-half the square of the one-loop amplitude, suggesting an exponential structure for IR divergences. The difference between the two-loop amplitude and one-half the square of the full one-loop amplitude is therefore finite, and expressible in a relatively simple form. We give arguments for generalizations to higher loops and n-point functions, suggesting that the exponential of the full one-loop amplitude may be corrected, to low orders, by only simple finite terms.