In recent years, a new holographic paradigm has emerged in which simple theories of gravity in low dimensions are dual to statistical ensembles of quantum mechanical systems rather than particular quantum systems. This is a conceptual departure from the conventional holographic paradigm, particularly as realized in string theory. A hallmark of such averaged holographic dualities is the non-factorization of multi-boundary observables due to the presence of Euclidean wormholes in the bulk gravitational theory. However, more realistic holographic dualities in higher dimensions are not expected to fundamentally involve microscopic averaging. Nevertheless, there are apparently contributions to the semiclassical gravitational path integral that are associated with averaging in the boundary theory. In this talk I will attempt to reconcile these perspectives by elucidating the emergence of averaging in two different models based on recent works of mine: one top-down, the other bottom-up. In both cases, averaging of boundary degrees of freedom is an emergent phenomenon associated with the expansion around the semiclassical limit.

In this talk, we present progress towards generalizing on-shell kinematics and color-kinematics duality to curved spacetimes. First, we define a perturbatively calculable quantity—the on-shell correlator—which furnishes a unified description of particle dynamics in curved spacetime. Specializing to the cases of flat and anti-de Sitter space, on-shell correlators coincide precisely with on-shell scattering amplitudes and boundary correlators respectively. We then introduce a notion of on-shell kinematics for symmetric spaces in which the corresponding on-shell momenta are built from isometry generators. Using this isometric language in AdS, we compute scalar correlators and give a field-theoretic derivation of color-kinematics duality for the nonlinear sigma model. Finally, we comment on possible extensions to spacetimes without symmetry.