Towards Color-Kinematics Duality in Generic Spacetimes

TL;DR

This paper explores the extension of color-kinematics duality to curved spacetimes, demonstrating its validity in specific models and establishing a double copy procedure in a curved background.

Contribution

It introduces a contact representation for on-shell correlators in curved spacetime, generalizing flat space kinematic features and confirming duality in the nonlinear sigma model.

Findings

Color-kinematics duality holds in generic spacetimes.

A double copy procedure connects different theories in curved space.

The approach applies to AdS transition amplitudes.

Abstract

In this note, we study color-kinematics duality in generic spacetimes. We work with a contact representation for on shell correlators. The position-space integrand is encoded by enumerated differential operators. This setup generalizes certain features of S-matrix kinematics to curved space. Differences between flat and curved space are captured by commutators. We study the nonlinear sigma model at four points as an explicit example and find that color-kinematics duality holds in generic spacetimes. We illustrate our approach in the AdS transition amplitude, a type of on shell correlation function. We find a double copy procedure at four points that connects the nonlinear sigma model, the biadjoint scalar theory, and the special Galileon theory.