The quantum strip: Liouville theory for open strings |
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Authors: | Eugène Cremmer Jean-Loup Gervais |
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Affiliation: | (1) Laboratoire de Physique Théorique de l'École Normale Supeieure, 24, rue Lhomond, F-75231 Paris Cedex 05, France;(2) Present address: Unité Propre du Centre National de la Recherche Scientifique, associée à l'École Normale Supérieure et à l'Université de Paris-Sud, Paris, France |
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Abstract: | The quantum group structure of 2D gravity recently put forward by one of us (J.-L. G.) is used to study quantum gravity on the strip. The boundary conditions, previously studied by A. Neveu and this author become easy to implement when one introduces the universal family of chiral operators associated withUq(sl(2)). A general formula for inverse powers of the metric-tensor operator is thereby derived. It contains a new universal matrixA, acting in representation-space, which obeys identities involving theR matrix, the Clebsch-Gordon coefficients, and the co-products ofUq(sl(2)). The physical meaning of these identities is to ensure that these powers of the metric are local and closed by fusion. |
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