comments on string theory on AdS₃

We study string propagation on AdSs times a compact space from an "old fashioned" worldsheet point of view of perturbative string theory. We derive the spacetime CFT and its Virasoro and current algebras, thus establishing the conjectured AdS/CFT correspondence for this case in the full string theory. Our results have implications for the extreme IR limit of the Dl -D5 system, as well as to 2+1 dimensional BTZ black holes and their Bekenstein-Hawking entropy.