Superconformal Algebras in Light-cone Gauge Quantization of String Theories on $AdS_3

Motivated by superstring theories on $AdS_3$, we construct spacetime superconformal algebras (SCAs) living on the $AdS_3$ boundary in terms of the transversal physical degrees of freedom. The SCAs constructed are N=4 large, middle algebras, and N=3 algebra, corresponding to superstring theories on $AdS_3 \times S ^3 \times S^3 \times S ^1$, $AdS_3 \times S ^3 \times T ^4$ and $AdS_3 \times (S^3\times S^3\times S^1)/Z_2$ backgrounds respectively.