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BRST analysis of physical states for 2D gravity coupled toc≦1 matter

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Abstract

We consider 2D gravity coupled toc≦1 conformal matter in the conformal gauge. The Liouville system is represented by a free scalar field,φ L, with background charge such that the BRST operator imposing reparametrization invariance is nilpotent. We compute the cohomology of this BRST charge on the product of the Fock space ofφ L with those of the ghosts and one other free scalar field,φ M representing the matter system. From this calculation the physical states of the full theory are determined. For thec<1 case the further projection from the Fock space ofφ M to the irreducible representation, using Felder's resolution, reproduces the results of Lian and Zuckerman.

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Authors and Affiliations

  1. CERN-Theory Division, CH-1211, Geneva 23, Switzerland

    Peter Bouwknegt

  2. Department of Physics, Brandeis University, 02254, Waltham, MA, USA

    Jim McCarthy & Krzysztof Pilch

  3. Department of Physics, University of Southern California, 90089-0484, Los Angeles, CA, USA

    Peter Bouwknegt, Jim McCarthy & Krzysztof Pilch

Authors
  1. Peter Bouwknegt
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  2. Jim McCarthy
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  3. Krzysztof Pilch
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Additional information

Communicated by K. Gawedzki

Supported by the NSF Grant # PHY-88-04561

Supported in part by the Department of Energy Contract # DE-FG03-84ER-40168 and by the USC Faculty Research and Innovation Fund

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Bouwknegt, P., McCarthy, J. & Pilch, K. BRST analysis of physical states for 2D gravity coupled toc≦1 matter. Commun.Math. Phys. 145, 541–560 (1992). https://doi.org/10.1007/BF02099397

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  • DOI: https://doi.org/10.1007/BF02099397

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