Hilbert Space of Space - time SCFT in AdS 3 Supersting and T 4 kp / S kp SCFT

We explore the superstring theory on AdS3 × S3 × T 4 in the framework given in [1]. We argue on the Hilbert space of “space-time CFT”, especially, construct a suitable vacuum of this CFT from the physical degrees of freedom of the superstring theory in bulk. We first construct explicitly it in the case of p = 1, and then present a proposal for the general cases of p > 1. After giving some completion of the GKS’s calculations about the higher mode operators (in particular, about the part including spin fields), we also present some comparison between the space-time CFT and T /Skp SCFT, namely, with respect to the physical spectrum of chiral primaries and some algebraic structures of bosonic and fermionic oscillators in both theories. We also observe how our proposal about the Hilbert space of space-time CFT can lead to a satisfactory correspondence between the spectrum of chiral primaries in both theories in the cases p > 1.