Quantum chaos and topology New perspectives on low-dimensional quantum gravity

What properties of a microscopic model of quantum gravity give rise to Einstein's laws of gravity at macroscopic distances? This PhD thesis addresses the above question in the controlled theoretical framework of the anti-de Sitter / conformal field theory (AdS/CFT) correspondence. Using tools from the theory of many-body quantum chaos, new evidence is given for the case that the semiclassical gravitational path integral (and the sum over topologies) computes a statistical average over pseudo-random microscopic CFT data. Special emphasis is placed on gravity in three spacetime dimensions, which, thanks to its exact solvability, provides an excellent testing ground for the ideas presented in this thesis. After introducing the proposed statistical framework in Part I, Part II is concerned with the statistics of black hole microstates and mixed state ensembles. Part III examines the statistics of heavy operators through the operator product expansion (OPE), while Part IV is focused on the spectral statistics of Virasoro primary states. In each part, the statistical predictions for products of CFT observables are matched to exact quantum gravity computations on multiboundary wormholes with asymptotically AdS boundary components. These computations point towards an averaged version of the holographic correspondence.