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

Abstract

We define a perturbatively calculable quantity--the on-shell\ncorrelator--which furnishes a unified description of particle dynamics in\ncurved spacetime. Specializing to the case of flat and anti-de Sitter space,\non-shell correlators coincide precisely with on-shell scattering amplitudes and\nboundary correlators, respectively. Remarkably, we find that symmetric\nmanifolds admit a generalization of on-shell kinematics in which the\ncorresponding momenta are literally the isometry generators of the spacetime\nacting on the external kinematic data. These isometric momenta are\nintrinsically non-commutative but exhibit on-shell conditions that are\nidentical to those of flat space, thus providing a common language for\ncomputing and representing on-shell correlators which is agnostic about the\nunderlying geometry. Afterwards, we compute tree-level on-shell correlators for\nbiadjoint scalar (BAS) theory and the nonlinear sigma model (NLSM) and learn\nthat color-kinematics duality is manifested at the level of fields under a\nmapping of the color algebra to the algebra of gauged isometries on the\nspacetime manifold. Last but not least, we present a field theoretic derivation\nof the fundamental BCJ relations for on-shell correlators following from the\nexistence of certain conserved currents in BAS theory and the NLSM.\n