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

TL;DR

This paper demonstrates an ABDK-like relation between the one- and two-loop four-graviton amplitudes in N=8 supergravity, showing that the IR-divergent part of the two-loop amplitude is the same as the divergent part of one-half the square of the one-loop amplitude. The finite remainder is surprisingly simple and expressible in terms of polylogarithms and zeta values, suggesting an exponential structure for IR divergences. Through a heuristic analysis, the authors argue that similar exponentiation controlled by the one-loop amplitude may extend to higher loops and to n-point functions, though without the fixed dual conformal symmetry of gauge theories. The work connects gravity amplitudes to gauge-theory structures via KLT relations and motivates further exploration of all-order IR behavior and finite remainders in N=8 supergravity.

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.