The No-Triangle Hypothesis for N=8 Supergravity

TL;DR

This paper provides evidence supporting the no-triangle hypothesis in N=8 supergravity, demonstrating that one-loop graviton amplitudes are composed solely of scalar box integrals, with proofs at six points and support for higher points.

Contribution

The paper offers a direct proof of the no-triangle hypothesis at six points and extends support for seven-point and higher amplitudes in N=8 supergravity.

Findings

Proof of no-triangle hypothesis at six points

Support for the hypothesis at seven points and beyond

One-loop graviton amplitudes contain only scalar box integrals

Abstract

We study the perturbative expansion of N=8 supergravity in four dimensions from the viewpoint of the ``no-triangle'' hypothesis, which states that one-loop graviton amplitudes in N=8 supergravity only contain scalar box integral functions. Our computations constitute a direct proof at six-points and support the no-triangle conjecture for seven-point amplitudes and beyond.