N=8 Supergravity 4-point Amplitudes

TL;DR

This paper provides explicit expressions for 4-point amplitudes in N=8 supergravity, explores potential 3-loop divergences, and investigates symmetry properties that could influence the theory's finiteness at higher loops.

Contribution

It offers the first explicit formulas for bosonic 4-particle amplitudes in N=8 supergravity, including higher-loop counterterms and symmetry analyses.

Findings

Explicit 4-point tree and 1-loop amplitudes including vectors and scalars.

Candidate 4-point UV divergences at 3-loop level expressed as helicity amplitudes.

Both 3-loop counterterms and 1-loop UV finite amplitudes exhibit unbroken E7 symmetry.

Abstract

We present the explicit expressions in N=8 supergravity for the bosonic 4-particle tree and 1-loop amplitudes including vectors and scalars. We also present the candidate 4-point UV divergences in a form of helicity amplitudes, corresponding to 3-loop manifestly N=8 supersymmetric and Lorentz covariant counterterm. This may shed some light on the 3-loop finiteness of N=8 SG and on a conjectured higher loop finiteness. We perform a supersymmetric deformation to complex momentum of the 4-point generating function including higher-loop counterterms and the 1-loop UV finite amplitudes. Using the explicit form of the scalar part of the 3-loop counterterm and of the 1-loop UV finite scalar 4-point amplitudes we find that they both have an unbroken E7 symmetry. We derive from E7 symmetry the low-energy theorem for the 1-loop n-point amplitudes.