Virtuous Trees at Five and Six Points for Yang-Mills and Gravity

TL;DR

This paper introduces a novel D-dimensional graph-based representation of five-point tree-level gluon amplitudes that satisfies key theoretical virtues and connects to multiloop structures, with a simpler six-point version in four dimensions.

Contribution

It presents a new D-dimensional representation of five-point amplitudes satisfying the color-kinematic correspondence and permutation symmetry, linking to multiloop structures.

Findings

The five-point amplitude representation satisfies color-kinematic duality.

It enables straightforward derivation of gravity amplitudes from gauge theory.

A six-point MHV amplitude representation is also provided in four dimensions.

Abstract

We present a particularly nice D-dimensional graph-based representation of the full color-dressed five-point tree-level gluon amplitude. It possesses the following virtues: 1) it satisfies the color-kinematic correspondence, and thus trivially generates the associated five-point graviton amplitude, 2) all external state information is encoded in color-ordered partial amplitudes, and 3) one function determines the kinematic contribution of all graphs in the Yang-Mills amplitude, so the associated gravity amplitude is manifestly permutation symmetric. The third virtue, while shared among all known loop-level correspondence-satisfying representations, is novel for tree-level representations sharing the first two virtues. This new D-dimensional representation makes contact with the recently found multiloop five-point representations, suggesting all-loop, all-multiplicity ramifications through unitarity. Additionally we present a slightly less virtuous representation of the six-point MHV and MHVbar amplitudes which holds only in four dimensions.