Holographic torus correlators in AdS3/CFT2

Abstract

In this talk, we will discuss holographic correlators of a CFT on a torus in both the pure gravitational system and the Einstein-scalar system within the framework of AdS3/CFT2. We perturbatively solve Einstein's equation near the conformal boundary and obtain holographic correlators through the variational principle. A holographic recurrence algorithm is developed to calculate higher-point stress tensor correlators. Additionally, we extend our computation program to investigate torus correlators in cutoff-AdS/TTbar-CFT holography and derive a parallel recurrence relation. After providing a detailed analysis of the pure gravity case, our attention is redirected towards investigating the holographic correlators in the Einstein-scalar system. We compute the correlators involving a mixed insertion of both the stress tensor and the dual scalar operator, and derive holographic torus Ward identities. The outcomes derived from the holographic approach align with established findings in CFTs, representing a significant confirmation of the AdS3/CFT2 correspondence.