SL (2, R) coset constructions and two-dimensional gravity

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Scientific paper

The relation between coset constructions of SL(2, R)/SO(1,1) and SL(2, R)/U(1) and the theories of two-dimensional gravity coupled to conformal matters is discussed, using the free field representations of the former. We find that both the topological gravity theory and the theory of c=1 conformal matter coupled to 2D gravity can be viewed as coset constructions of SL(2,R) current algebra. We also compare these results with 2D black hole theory.
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