Pure Anti-de Sitter Supergravity and the Conformal Bootstrap

We consider graviton scattering in maximal supergravity on anti-de Sitter space (AdS) in d+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}×S^{5} dual to N=4 super-Yang-Mills, where the CFT has light single trace operators for each Kaluza-Klein mode on S^{5}. 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 M-theory duals all lie inside the allowed region.