Pure Anti-de Sitter Supergravity and the Conformal Bootstrap

We consider graviton scattering in maximal supergravity on anti-de Sitter space (AdS) in d thorn 1 dimensions for d = 3, 4, and 6 with no extra compact spacetime factor. Holography suggests that this theory is dual to an exotic maximally supersymmetric conformal field theory (CFT) in d dimensions whose only light single trace operator is the stress tensor. This contrasts with more standard cases like type IIB string theory on AdS 5 x S-5 dual to N = 4 super-Yang-Mills, where the CFT has light single trace operators for each Kaluza-Klein mode on S5. We compute the one-loop correction to the pure AdS(d+1) theory in a small Planck length expansion, which is dual to the large central charge expansion in the CFT. We find that this correction saturates the most general nonperturbative conformal bootstrap bounds on this correlator in the large central charge regime for d = 3, 4, 6, while the one-loop correction to CFTs with string and Mtheory duals all lie inside the allowed region.

Automated summary

This article discusses graviton scattering in maximal supergravity and investigates the one-loop correction of the corresponding conformal field theory in AdS space. The research finds that for certain dimensions, the correction saturates the conformal bootstrap bounds, while the corrections in conformal field theories with string and M-theory duals lie within the allowed region.