On-shell correlators and color-kinematics duality in curved symmetric spacetimes

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