New Relations for Gauge-Theory Amplitudes

TL;DR

This paper introduces a new kinematic identity for gauge-theory amplitudes that reveals novel relations between color-ordered amplitudes and offers insights into gravity amplitudes, aiding multi-loop calculations.

Contribution

It presents a kinematic analog of the Jacobi identity, leading to new amplitude relations and a reorganization of gravity amplitudes, enhancing understanding of gauge-gravity connections.

Findings

Derived a kinematic Jacobi-like identity.

Established new relations between partial amplitudes.

Reorganized gravity amplitudes to reveal structural insights.

Abstract

We present an identity satisfied by the kinematic factors of diagrams describing the tree amplitudes of massless gauge theories. This identity is a kinematic analog of the Jacobi identity for color factors. Using this we find new relations between color-ordered partial amplitudes. We discuss applications to multi-loop calculations via the unitarity method. In particular, we illustrate the relations between different contributions to a two-loop four-point QCD amplitude. We also use this identity to reorganize gravity tree amplitudes diagram by diagram, offering new insight into the structure of the KLT relations between gauge and gravity tree amplitudes. This can be used to obtain novel relations similar to the KLT ones. We expect this to be helpful in higher-loop studies of the ultraviolet properties of gravity theories.