One-loop N=8 Supergravity Amplitudes from MHV Diagrams

TL;DR

This paper develops a method to compute one-loop N=8 supergravity amplitudes using MHV diagrams by introducing spinor shifts to handle off-shell gravitons, successfully reproducing known four-point results and extending to multiple gravitons.

Contribution

It introduces a novel off-shell prescription for MHV diagrams in supergravity, enabling the calculation of one-loop graviton amplitudes with arbitrary numbers of external particles.

Findings

Reproduces known four-point one-loop graviton amplitude.

Extends MHV diagram techniques to supergravity amplitudes.

Provides a framework for calculating multi-graviton loop amplitudes.

Abstract

We discuss the calculation of one-loop amplitudes in N=8 supergravity using MHV diagrams. In contrast to MHV amplitudes of gluons in Yang-Mills, tree-level MHV amplitudes of gravitons are not holomorphic in the spinor variables. In order to extend these amplitudes off shell, and use them as vertices to build loops, we introduce certain shifts for the spinor variables associated to the loop momenta. Using this off-shell prescription, we rederive the four-point MHV amplitude of gravitons at one loop, in complete agreement with known results. We also discuss the extension to the case of one-loop MHV amplitudes with an arbitrary number of gravitons.