Hidden SL(n) symmetry in conformal field theories

We prove that an irreducible representation of the Virasoro algebra can be extracted from an irreducible representation space of the SL(2, R) current algebra by putting a constraint on the latter using the Becchi-Rouet-Stora-Tyutin formalism. Thus there is a SL(2, R) symmetry in the Virasoro algebra, but it is gauged and hidden. This construction of the Virasoro algebra is the quantum analogue of the Hamiltonian reduction. We then are naturally lead to consider a constrained SL(2, R) Wess-Zumino-Witten model. This system is also related to quantum field theory of coadjoint orbit of the Virasoro group. Based on this result, we present a canonical derivation of the SL(2, R) current algebra in Polyakov's theory of two-dimensional gravity; it is a manifestation of the SL(2, R) symmetry in conformal field theory hidden by the quantum Hamiltonian reduction. We also discuss the quantum Hamiltonian reduction of the SL(n, R) current algebra and its relation to the Wn-algebra of Zamolodchikov. This makes it possible to define a natural generalization of the geometric action for the Wn-algebra despite its non-Lie-algebraic nature. (orig.)