Absence of Triangles in Maximal Supergravity Amplitudes

TL;DR

This paper proves that in maximal supergravity, one-loop n-point amplitudes contain only scalar box integrals, demonstrating cancellations beyond supersymmetry and supporting the no-triangle hypothesis.

Contribution

It introduces new reduction formulas for one-loop amplitudes in colourless theories, establishing the absence of triangle integrals in maximal supergravity.

Findings

Maximal supergravity amplitudes contain only scalar box integrals.

New reduction formulas reveal cancellations beyond supersymmetry.

Supports the no-triangle hypothesis in four-dimensional supergravity.

Abstract

From general arguments, we show that one-loop n-point amplitudes in colourless theories satisfy a new type of reduction formula. These lead to the existence of cancellations beyond supersymmetry. Using such reduction relations we prove the no-triangle hypothesis in maximal supergravity by showing that in four dimensions the n-point graviton amplitude contain only scalar box integral functions. We also discuss the reduction formulas in the context of gravity amplitudes with less and no supersymmetry.