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

Motivated by superstring theories on $Ad{S}_3$, we construct spacetime superconformal algebras (SCAs) living on the $Ad{S}_3$ 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 $Ad{S}_3\times S^3\times S^3\times S^1$, $Ad{S}_3\times S^3\times T^4$ and $Ad{S}_3\times (S^3\times S^3\times S^1)\mathrm{/}{Z}_2$ backgrounds respectively.