NB: non-standard time!

Title: Symmetry-weighted ensemble averaging from TQFT gravity

Abstract: In a recently proposed framework of TQFT gravity (2310.13044, 2405.20366) -- a toy model of AdS3 gravity -- a bulk 3d TQFT summed over all topologies is shown to be dual to a unitary ensemble of boundary 2d CFTs. I will show that the CFTs in this ensemble are weighted by the inverse of the order of their symmetry group (relative to the categorical symmetry provided by the bulk TQFT as a SymTFT). Mathematically, this is the natural measure over the groupoid of the TQFT Lagrangian algebras that construct the CFTs, and the holographic duality then provides a generalization of the Siegel-Weil formula beyond averaging over bosonic lattice-CFTs. I will also discuss some examples for rational CFTs as well as implications to noncompact TQFTs and pure gravity.

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.