Emergent space-time and the supersymmetric index

TL;DR

This paper investigates criteria within 2d CFTs, especially supersymmetric ones, that indicate the emergence of macroscopic 3d gravity via holography, using elliptic genus as a key diagnostic tool.

Contribution

It introduces the use of elliptic genus to identify when supersymmetric CFTs can produce large radius gravity in holographic duals, highlighting new classes of theories with this property.

Findings

Elliptic genus can signal emergent gravity with large radius in supersymmetric CFTs.

Certain constructions suggest gravity with Planck length much smaller than string length and AdS radius.

Large N symmetric orbifolds are consistent with emergent space-time string theories.

Abstract

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.