Recursion Relations for One-Loop Gravity Amplitudes

TL;DR

This paper demonstrates how recursion relations can be used to compute certain finite one-loop gravity amplitudes, revealing both successes and challenges in extending these methods to more complex cases.

Contribution

It introduces recursion relations for calculating finite one-loop gravity amplitudes and explores their application to specific helicity configurations, including a new one-loop three-point vertex.

Findings

Successfully derived known four, five, and six graviton amplitudes using recursion relations.

Identified difficulties in applying recursion to the five-point amplitude with helicities (-,+,+,+,+).

Proposed potential resolutions for issues encountered in complex amplitude calculations.

Abstract

We study the application of recursion relations to the calculation of finite one-loop gravity amplitudes. It is shown explicitly that the known four, five, and six graviton one-loop amplitudes for which the external legs have identical outgoing helicities, and the four graviton amplitude with helicities (-,+,+,+) can be derived from simple recursion relations. The latter amplitude is derived by introducing a one-loop three-point vertex of gravitons of positive helicity, which is the counterpart in gravity of the one-loop three-plus vertex in Yang-Mills. We show that new issues arise for the five point amplitude with helicities (-,+,+,+,+), where the application of known methods does not appear to work, and we discuss possible resolutions.