Anatoly Dymarsky - TQFT Gravity and Ensemble Holography

03/14/2025
Abstract: Recent advances in quantum gravity have raised the question whether holographic correspondence relates quantum gravity to a single boundary theory or an ensemble. We propose a TQFT gravity framework where bulk TQFTs summed over all possible topologies correspond holographically to ensembles of boundary theories. We prove the unitarity of these boundary ensembles and demonstrate that many (if not all) known examples of ensemble holography fit within this framework. We present explicit Abelian and non-Abelian examples and suggest how this approach might help calculate the partition function of pure 3d quantum gravity in AdS₃. This talk is based on 2405.20366, 2310.13044, earlier papers, and ongoing work.