Emergent space-time and the supersymmetric index

It is of interest to find criteria on a 2d CFT which indicate that it gives rise to emergent gravity in a macroscopic 3d AdS space via holography. Symmetric orbifolds in the large N limit have partition functions which are consistent with an emergent space-time string theory with L-string similar to L-AdS. For supersymmetric CFTs, the elliptic genus can serve as a sensitive probe of whether the SCFT admits a large radius gravity description with L-string << L-AdS after one deforms away from the symmetric orbifold point in moduli space. We discuss several classes of constructions whose elliptic genera strongly hint that gravity with L-Planck << L-string << L-AdS can emerge at suitable points in moduli space.