Graphs, determinants and gravity amplitudes

TL;DR

This paper uses the matrix-tree theorem to connect diagrammatic and determinant expressions in gravity scattering amplitudes, providing new formulations and proofs for MHV amplitudes and recasting one-loop supergravity results.

Contribution

It introduces a graph-theoretical framework for gravity amplitudes and proves new identities, linking different mathematical representations in the field.

Findings

Established a general graph-theoretical formulation for MHV gravity amplitudes

Proved two identities for half-soft functions in gravity amplitudes

Recast one-loop supergravity rational parts into matrix form

Abstract

We apply the matrix-tree theorem to establish a link between various diagrammatic and determinant expressions, which naturally appear in scattering amplitudes of gravity theories. Using this link we are able to give a general graph-theoretical formulation for the tree-level maximally-helicity-violated gravity amplitudes. Furthermore, we use the link to prove two identities for half-soft functions of gravity amplitudes. Finally we recast the diagrammatic formulation of one-loop rational part of $\mathcal{N}=4$ supergravity into a matrix form.