Quantum gravity on AdS3×S3 from CFT: bootstrapping n = 21

A

bstract

We consider the simplest four-point scattering amplitude of SO( n ) tensor multiplets in six-dimensional (2,0) supergravity on AdS ₃ ×S ³ . Using crossing symmetry and the consistency of the operator product expansion in the dual CFT, we explicitly construct the one-loop contribution to the correlator at order 1/ c ² , both in position space and in Mellin space. We show that a strong form of the bootstrap equations imposes constraints on the value of n . Remarkably, we find that our bootstrap approach uniquely determines n = 21, which corresponds to the spectrum of IIB string theory compactified on K3. This stands in sharp contrast to the tree-level correlator for which n is unconstrained. We also analyse the spectrum of unprotected double-trace operators and solve the mixing problem in the first case that involves both tensor and graviton correlators. When n = 21, the anomalous dimensions rationalise and one of them vanishes. Lastly, we study the flat-space limit of the correlator and find perfect agreement with the one-loop amplitude recently obtained in [1].