Gravity On-shell Diagrams

TL;DR

This paper develops a Grassmannian formula for gravity on-shell diagrams, revealing unique features like non-trivial numerators and higher degree poles, and explores their implications for loop amplitudes and singularities.

Contribution

It introduces a novel Grassmannian representation for gravity on-shell diagrams, highlighting differences from gauge theory and conjecturing properties of gravity loop amplitudes.

Findings

Gravity on-shell diagrams have a Grassmannian formula with non-trivial numerators.

Loop amplitudes exhibit only logarithmic singularities on finite cuts.

Cancellations are crucial for the behavior on collinear cuts in loop amplitudes.

Abstract

We study on-shell diagrams for gravity theories with any number of supersymmetries and find a compact Grassmannian formula in terms of edge variables of the graphs. Unlike in gauge theory where the analogous form involves only $\dlog$-factors, in gravity there is a non-trivial numerator as well as higher degree poles in the edge variables. Based on the structure of the Grassmannian formula for $\N=8$ supergravity we conjecture that gravity loop amplitudes also possess similar properties. In particular, we find that there are only logarithmic singularities on cuts with finite loop momentum, poles at infinity are present and loop amplitudes show special behavior on certain collinear cuts. We demonstrate on 1-loop and 2-loop examples that the behavior on collinear cuts is a highly non-trivial property which requires cancellations between all terms contributing to the amplitude.