On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes

TL;DR

This paper introduces on-shell correlators in curved symmetric spacetimes, unifying particle dynamics and revealing a generalized kinematic framework that extends flat space concepts to curved geometries, and explores color-kinematics duality.

Contribution

It defines on-shell correlators in curved spacetimes, generalizes on-shell kinematics via isometry generators, and demonstrates color-kinematics duality and BCJ relations in this context.

Findings

On-shell correlators coincide with scattering amplitudes and boundary correlators in flat and AdS spaces.

Generalized on-shell kinematics uses isometry generators acting on external data.

Color-kinematics duality is realized through the algebra of gauged isometries.

Abstract

We define a perturbatively calculable quantity--the on-shell correlator--which furnishes a unified description of particle dynamics in curved spacetime. Specializing to the case of flat and anti-de Sitter space, on-shell correlators coincide precisely with on-shell scattering amplitudes and boundary correlators, respectively. Remarkably, we find that symmetric manifolds admit a generalization of on-shell kinematics in which the corresponding momenta are literally the isometry generators of the spacetime acting on the external kinematic data. These isometric momenta are intrinsically non-commutative but exhibit on-shell conditions that are identical to those of flat space, thus providing a common language for computing and representing on-shell correlators which is agnostic about the underlying geometry. Afterwards, we compute tree-level on-shell correlators for biadjoint scalar (BAS) theory and the nonlinear sigma model (NLSM) and learn that color-kinematics duality is manifested at the level of fields under a mapping of the color algebra to the algebra of gauged isometries on the spacetime manifold. Last but not least, we present a field theoretic derivation of the fundamental BCJ relations for on-shell correlators following from the existence of certain conserved currents in BAS theory and the NLSM.