Explicit Cancellation of Triangles in One-loop Gravity Amplitudes

TL;DR

This paper investigates one-loop gravity amplitudes, revealing the absence of triangle contributions in certain cases, and links these cancellations to coordinate invariance, which enhances the understanding of supergravity's ultraviolet properties.

Contribution

It demonstrates explicit triangle cancellations in one-loop gravity amplitudes and connects these to coordinate invariance, advancing the understanding of supergravity ultraviolet behavior.

Findings

No triangle contributions in five-graviton one-loop amplitudes.

Cancellations linked to general coordinate invariance.

Implications for improved high-energy behavior of gravity amplitudes.

Abstract

We analyse one-loop graviton amplitudes in the field theory limit of a genus-one string theory computation. The considered amplitudes can be dimensionally reduced to lower dimensions preserving maximal supersymmetry. The particular case of the one-loop five-graviton amplitude is worked out in detail and explicitly features no triangle contributions. Based on a recursive form of the one-loop amplitude we investigate the contributions that will occur at n-point order in relation to the ``no-triangle'' hypothesis of N=8 supergravity. We argue that the origin of unexpected cancellations observed in gravity scattering amplitudes is linked to general coordinate invariance of the gravitational action and the summation over all orderings of external legs. Such cancellations are instrumental in the extraordinary good ultra-violet behaviour of N=8 supergravity amplitudes and will play a central role in improving the high-energy behaviour of gravity amplitudes at more than one loop.