The paper derives a closed all-orders formula for the leading high-energy part of the N=8 supergravity remainder function, confirming the recent three-loop calculation and predicting new terms at four loops and beyond.
Two-loop graviton scattering relation and IR behavior in N=8 supergravity
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abstract
We derive an ABDK-like relation between the one- and two-loop four-graviton amplitudes in N=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.
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A tale of two exponentiations in ${\cal N}=8$ supergravity
The paper derives a closed all-orders formula for the leading high-energy part of the N=8 supergravity remainder function, confirming the recent three-loop calculation and predicting new terms at four loops and beyond.