Light-Cone Gauge Quantization of String Theories on $AdS_3$ Space

Light-cone gauge quantization procedures are given, for superstring theory on $AdS_3$ space charged with NS-NS background, both in NSR and GS formalism. The spacetime (super)conformal algebras are constructed in terms of the transversal physical degrees of freedom. The spacetime conformal anomaly agrees with that of covariant formalism, provided that the worldsheet conformal anomaly $c$ equals 26 or 15 for bosonic string or superstring, respectively. The spacetime (super)conformal field theory is found to correspond to orbifold construction on symmetric product space $\it{Sym_p} {\cal{M}}/Z_p$.