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 $L_{\rm string} \sim L_{\rm AdS}$. For supersymmetric CFTs, the elliptic genus can serve as a sensitive probe of whether the SCFT admits a large radius gravity description with $L_{\rm string} \ll L_{\rm AdS}$ 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 $L_{\rm Planck} \ll L_{\rm string} \ll L_{\rm AdS}$ can emerge at suitable points in moduli space.

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