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Local BRST cohomology in the antifield formalism: II. Application to Yang-Mills theory

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Abstract

Yang-Mills models with compact gauge group coupled to matter fields are considered. The general tools developed in a companion paper are applied to compute the local cohomology of the BRST differentials modulo the exterior space-time derivatived for all values of the ghost number, in the space of polynomials in the fields, the ghosts, the antifields (=sources for the BRST variations) and their derivatives. New solutions to the consistency conditionssa+db=0 depending non-trivially on the antifields are exhibited. For a semi-simple gauge group, however, these new solutions arise only at ghost number two or higher. Thus at ghost number zero or one, the inclusion of the antifields does not bring in new solutions to the consistency conditionsa+db=0 besides the already known ones. The analysis does not use power counting and is purely cohomological. It can be easily extended to more general actions containing higher derivatives of the curvature or Chern-Simons terms.

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Author notes

  1. Friedemann Brandt

    Present address: Instituut voor Theoretische Fysica, K.U. Leuven, Celestijnenlaan 200D, B-3001, Leuven, Belgium

  2. Glenn Barnich (Aspirant)

    Present address: Fonds National de la Recherche Scientifique, Belgium

  3. Marc Henneaux

    Present address: Centro de Estudios Científicos de Santiago, Chile

Authors and Affiliations

  1. Faculté des Sciences, Université Libre de Bruxelles, Campus Plaine C.P. 231, B-1050, Bruxelles, Belgium

    Glenn Barnich (Aspirant) & Marc Henneaux

  2. NIKHEF-H, Postbus 41882, NL-1009 DB, Amsterdam, The Netherlands

    Friedemann Brandt

Authors
  1. Glenn Barnich
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  2. Friedemann Brandt
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  3. Marc Henneaux
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Additional information

Communicated by G. Felder

Supported by Deutsche Forschungsgemeinschaft and by the research council (DOC) of the K.U. Leuven.

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Barnich, G., Brandt, F. & Henneaux, M. Local BRST cohomology in the antifield formalism: II. Application to Yang-Mills theory. Commun.Math. Phys. 174, 93–116 (1995). https://doi.org/10.1007/BF02099465

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  • DOI: https://doi.org/10.1007/BF02099465

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