I will describe a CFT framework for reproducing computations done with the Euclidean path integral of semi-classical Einstein gravity. This framework called "OPE Randomness Hypothesis" is a generalization of the eigenstate thermalization hypothesis, where OPE coefficients involving heavy operators are treated as random variables. I will show how this explains the appearance of Euclidean wormholes in the gravitational path integral, resolving a puzzle first presented by Maoz and Maldacena. I will then discuss the role that global symmetries play in this framework and generalize the ETH to include such symmetries. I will show that the existence of Euclidean wormholes prevents exact global symmetries in quantum gravity: they must either be gauged or broken by non-perturbative effects.