Quantum coherent string states in AdS(3) and the SL(2,R) Wess-Zumino-Witten-Novikov model - art. no. 046003

In this paper we make the connection between semiclassical string quantizat ion and exact conformal field theory quantization of strings in 2+1 anti-de Sitter spacetime. More precisely, considering the Weiss-Zumino-Witten-Novi kov model corresponding to SL(2,R) and its covering group, we construct qua ntum 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 t achyonic) satisfying the standard spin-level condition necessary for unitar ity \j\<k/2, and a discrete spectrum of high mass states with asymptotic be havior m(2) alpha' proportional to N-2 (N positive integer). The quantizati on condition for the high mass states arises from the condition of finite p ositive norm of the coherent string states, and the result agrees with our previous results obtained using semiclassical quantization. In the k --> (i nfinity) limit, all the usual properties of coherent or quasiclassical stat es are recovered. It should be stressed that we consider the circular strin gs 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 paper by Maldacena and Ooguri, hep-th/0001053 .