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In recent work we computed the path integral of three-dimensional gravitywith negative cosmological constant on spaces which are topologically a torustimes an interval. Here we employ a modular bootstrap to show that theamplitude is completely fixed by consistency conditions and a few basic inputsfrom gravity. This bootstrap is notably for an ensemble of CFTs, rather thanfor a single instance. We also compare the 3d gravity result with the Narainensemble. The former is well-approximated at low temperature by a random matrixtheory ansatz, and we conjecture that this behavior is generic for an ensembleof CFTs at large central charge with a chaotic spectrum of heavy operators.

AdS$_3$ wormholes from a modular bootstrap