Abstract
It is shown that Liouville theory can be regarded as an SL(2, ø) Wess-Zumino-Novikov-Witten theory with conformal invariant constraints and that Polyakov's SL(2, ø) Kac-Moody symmetry of induced two-dimensional gravity is just one side of the WZNW current algebra. Analogously, Toda field theories can be regarded as conformal-invariantly constrained WZNW theories for appropriate (maximally non-compact) groups.
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