Pure Gravities via Color-Kinematics Duality for Fundamental Matter

TL;DR

This paper develops a method to compute loop-level scattering amplitudes in pure Einstein gravity and supergravities using color-kinematics duality, incorporating fundamental matter as ghosts to cancel unwanted states.

Contribution

It extends color-kinematics duality to fundamental matter and provides a new prescription for calculating supergravity amplitudes with arbitrary non-self-interacting matter.

Findings

Constructed amplitudes using double copies of pure Yang-Mills and fundamental matter.

Extended color-kinematics duality to fundamental representations.

Validated the approach with explicit tree and loop amplitude calculations.

Abstract

We give a prescription for the computation of loop-level scattering amplitudes in pure Einstein gravity, and four-dimensional pure supergravities, using the color-kinematics duality. Amplitudes are constructed using double copies of pure (super-)Yang-Mills parts and additional contributions from double copies of fundamental matter, which are treated as ghosts. The opposite-statistics states cancel the unwanted dilaton and axion in the bosonic theory, as well as the extra matter supermultiplets in supergravities. As a spinoff, we obtain a prescription for obtaining amplitudes in supergravities with arbitrary non-self-interacting matter. As a prerequisite, we extend the color-kinematics duality from the adjoint to the fundamental representation of the gauge group. We explain the numerator relations that the fundamental kinematic Lie algebra should satisfy. We give nontrivial evidence supporting our construction using explicit tree and loop amplitudes, as well as more general arguments.