Sub-AdS Scale Locality in AdS$_3$/CFT$_2$

TL;DR

This paper studies sub-AdS scale locality in a simple AdS$_3$/CFT$_2$ model, showing it matches gravity expectations at leading order and suggesting general conditions for such dualities.

Contribution

It demonstrates that a weakly coupled AdS$_3$/CFT$_2$ model exhibits correct density of states and correlation functions, and proposes criteria for sub-AdS locality in large N CFT$_2$.

Findings

Model has correct low and high energy density of states.

Bulk correlators match gravity at leading order.

Non-local effects appear at order 1/N.

Abstract

We investigate sub-AdS scale locality in a weakly coupled toy model of the AdS$_3$/CFT$_2$ 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 AdS$_3$. Bulk correlation functions also have the correct behavior at leading order in the large $N$ expansion, but non-local effects emerge at order $1/N$. Our analysis leads to the conjecture that any large $N$ CFT$_2$ that is modular invariant and has the right low-energy density of states is dual to a gravitational theory with sub-AdS scale locality.