On AdS3 String Theory

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String theory on curved backgrounds has received much attention on account of both its own interest, and of its relation with gauge theories. Despite the progress made in various directions, several quite elementary questions remain unanswered, in particular in the very simple case of three-dimensional anti-de Sitter space. I briefly review these problems.
5 pages, latex + cargese.cls. To appear in the proceedings of the Cargese 99 NATO-ASI. Strict summary of a more extended version hep-th/9908189

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