Sub-AdS scale locality in AdS3/CFT2

We investigate sub-AdS scale locality in a weakly coupled toy model of the AdS3/CFT2 correspondence. We find that this simple model has the correct density of states at low and high energies to be dual to Einstein gravity coupled to matter in AdS3. The bulk correlation functions also have the correct behavior at leading order in the large N expansion, but deviations appear at order 1/N . We interpret this as evidence for non-locality of the theory, which is consistent with the presence of an infinite tower of massless higher-spin fields. Finally, we conjecture that any large N CFT2 that is both modular invariant, and exhibits the correct low-energy density of states, is dual to a gravitational theory with sub-AdS scale locality.