Quantum Coherent String States in AdS_3 and SL(2,R) WZWN Model

TL;DR

This paper constructs quantum coherent string states in AdS_3 using the SL(2,R) WZWN model, linking semi-classical and exact conformal field theory quantizations, and analyzes their spectra and classical limits.

Contribution

It introduces a method to construct quantum coherent string states in AdS_3, connecting semi-classical and exact quantizations, and characterizes their spectra and classical behavior.

Findings

Spectrum includes low mass (tachyonic) and high mass states.

High mass states follow m^2α' ∝ N^2 behavior.

Classical limit recovers properties of coherent states.

Abstract

In this paper we make the connection between semi-classical string quantization and exact conformal field theory quantization of strings in 2+1 Anti de Sitter spacetime. More precisely, considering the WZWN model corresponding to SL(2,R) and its covering group, we construct quantum {\it coherent} string states, which generalize the ordinary coherent states of quantum mechanics, and show that in the classical limit they correspond to oscillating circular strings. After quantization, the spectrum is found to consist of two parts: A continuous spectrum of low mass states (partly tachyonic) fulfilling the standard spin-level condition necessary for unitarity |j|< k/2, and a discrete spectrum of high mass states with asymptotic behaviour m^2\alpha'\propto N^2 (N positive integer). The quantization condition for the high mass states arises from the condition of finite positive norm of the coherent string states, and the result agrees with our previous results obtained using semi-classical quantization. In the k\to\infty limit, all the usual properties of coherent or {\it quasi-classical} states are recovered. It should be stressed that we consider the circular strings only for simplicity and clarity, and that our construction can easily be used for other string configurations too. We also compare our results with those obtained in the recent preprint hep-th/0001053 by Maldacena and Ooguri.