Wormholes from heavy operator statistics in AdS/CFT

We construct higher dimensional euclidean AdS wormhole solutions that reproduce the statistical description of the correlation functions of an ensemble of heavy CFT operators. We consider an operator which effectively backreacts on the geometry in the form of a thin shell of dust particles. Assuming dynamical chaos in the form of the ETH ansatz, we demonstrate how semiclassical wormholes provide a statistical description of the matrix elements of the thin shell operator in the CFT. The wormhole solutions correspond to microcanonical saddle-points dominated by different energy bands of the CFT. We finally elaborate on the role of these wormholes in the context of non-perturbative violations of bulk global symmetries in AdS/CFT.Comment: 34 pages, 10 figure