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 ∼ 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.