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

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.

19 pages

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• Comments on black hole interiors and modular inclusions
• $\mathcal{N}=2$ Minimal Models: A Holographic Needle in a Symmetric Orbifold Haystack
• Black holes from CFT: Universality of correlators at large c
• The Stranger Things of Symmetric Product Orbifold CFTs
• Siegel Paramodular Forms and Sparseness in AdS${}_3$/CFT${}_2$
• Holographic phenomenology via overlapping degrees of freedom
• Precursors and BRST Symmetry