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

TL;DR

This paper constructs and analyzes the Hilbert space of space-time CFT for superstring theory on AdS_3 x S^3 x T^4, establishing a correspondence with T^{4kp}/S_{kp} SCFT and exploring spectrum and algebraic structures.

Contribution

It explicitly constructs the space-time CFT Hilbert space for p=1 and proposes a generalization for p>1, including completion of higher mode operators and spectrum comparison.

Findings

Constructed the vacuum state for p=1 case.

Proposed a generalization for p>1 cases.

Established spectrum correspondence between theories.

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.