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.