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BEYOND THE LARGE N LIMIT: NON-LINEAR W_∞ AS SYMMETRY OF THE SL(2,R)/U(1) COSET MODEL

Center for Theoretical Physics, Department of Physics and Astronomy, University of Maryland, College Park, MD 20742, USA

Address after September 16, 1991: School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA.

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ELIAS KIRITSIS

Department of Physics, University of California and Theoretical Physics Group, Lawrence Berkeley Laboratory, Berkeley, CA 94720, USA

Address after October 1, l991: Lab. de Physique Théorique, Ecole Normale Superieure, 34 rue, Lhomond, F-75231, Paris, CEDEX 05, FRANGE.

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https://doi.org/10.1142/S0217751X92003720Cited by:75 (Source: Crossref)

Abstract

We show that the symmetry algebra of the SL(2,R)_k/ U(1) coset model is a non-linear deformation of W_∞, characterized by k. This is a universal W-algebra which linearizes in the large k limit and truncates to W_N for K=-N. Using the theory of non-compact parafermions we construct a free field realization of the non-linear W_∞ in terms of two bosons with background charge. The W-characters of all unitary SL(2,R)/ U(1) representations are computed. Applications to the physics of 2-d black hole backgrounds are also discussed and connections with the KP approach to c=1 string theory are outlined.

This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grants PHY-85-15857 and PHY-87-17155.

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