Hilbert Space of Space-time SCFT in AdS_3 Supersting and T^{4kp}/S_{kp} SCFT

TL;DR

The paper addresses identifying the Hilbert space and vacuum of the space-time CFT dual to string theory on $AdS_3\times S^3\times T^4$, and proposes explicit constructions for the $p=1$ vacuum along with a general $p$-string extension. It develops a detailed world-sheet framework, builds the space-time $N=4$ SCA with central charge $c=6pk$, and introduces a second-quantized picture of the space-time CFT via $p$-string vacua. By constructing diagonal $T^4$ oscillators and analyzing chiral primaries, the authors establish a close correspondence with the symmetric orbifold CFT $T^{4kp}/S_{kp}$, including a level-enhancement mechanism in twisted sectors that resolves previous discrepancies. The results support a string-level realization of $AdS_3/CFT_2$ and point toward a Matrix-string-like formulation with potential applications to correlation functions and BTZ black-hole physics.

Abstract

We explore the superstring theory on AdS_3 x S^3 x T^4 in the framework given in hep-th/9806194. We argue on the Hilbert space of "space-time CFT", and especially construct a suitable vacuum of this CFT from the physical degrees of freedom of the superstring theory in bulk. We first construct it explicitly 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 constructions of the higher mode operators (in particular, of those including spin fields), we also make some comparison between the space-time CFT and T^{4kp}/S_{kp} 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 leads to a satisfactory correspondence between the spectrum of chiral primaries of both theories in the cases of p>1.