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

TL;DR

This paper establishes a relation between one- and two-loop four-graviton amplitudes in N=8 supergravity, revealing an exponential IR divergence structure and proposing a pattern for higher-loop corrections.

Contribution

It derives an ABDK-like relation in N=8 supergravity, showing the IR divergence structure and suggesting a simple exponential form for multi-loop amplitudes.

Findings

Infrared divergent part of two-loop amplitude is half the square of one-loop amplitude.

The difference between two-loop amplitude and half the square of one-loop amplitude is finite.

Proposes that higher-loop amplitudes may follow a similar exponential correction pattern.

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.