2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/198855We study string propagation on $AdS_3$ 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 $D1-D5$ system, as well as to 2+1 dimensional BTZ black holes and their Bekenstein-Hawking entropy.46 pages, harvmac; minor changes and references addedHigh Energy Physics - Theorytext