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Interesting nonperturbative CFT dualities like the FZZ duality between
the 2d black hole and Sine-Liouville can be
understood as a combination of two remarkable phenomena: The first is
the modular (self-)duality of Liouville or conformal Toda theory, the
second is the relation between Liouville theory and the sl_2-WZNW model.
The latter can be seen as a natural "quantum" analog of the
geometric Langlands duality. It may be reformulated as a correspondence
between quantum Teichmüller theory and the sl_2-WZNW model.
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