Fock representations and BRST cohomology inSL(2) current algebra |
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Authors: | D. Bernard G. Felder |
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Affiliation: | (1) Groupe d'Astrophysique Relativiste, CNRS, Observatoire de Meudon, F-92195 Meudon, France;(2) Service de Physique Théorique, CEN-Saclay, F-91191 Gif-sur-Yvette, France;(3) Institut für theoretische Physik, ETH Hönggerberg, CH-8093 Zürich, Switzerland |
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Abstract: | We investigate the structure of the Fock modules overA1(1) introduced by Wakimoto. We show that irreducible highest weight modules arise as degree zero cohomology groups in a BRST-like complex of Fock modules. Chiral primary fields are constructed as BRST invariant operators acting on Fock modules. As a result, we obtain a free field representation of correlation functions of theSU(2) WZW model on the plane and on the torus. We also consider representations of fractional level arising in Polyakov's 2D quantum gravity. Finally, we give a geometrical, Borel-Weil-like interpretation of the Wakimoto construction. |
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