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Results on the Wess-Zumino consistency condition for arbitrary Lie algebras

par Barkallil, Abdelilah ;Barnich, Glenn ;Schomblond, Christiane
Référence Journal of Mathematical Physics, 43, 12, page (5987-6015)
Publication Publié, 2002-05

Article révisé par les pairs

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Résumé :

The so-called covariant Poincaré lemma on the induced cohomology of the space-time exterior derivative in the cohomology of the gauge part of the BRST differential is extended to cover the case of arbitrary, nonreductive Lie algebras. As a consequence, the general solution of the Wess-Zumino consistency condition with a nontrivial descent can, for arbitrary (super) Lie algebras, be computed in the small algebra of the one-form potentials, the ghosts and their exterior derivatives. For particular Lie algebras that are the semidirect sum of a semisimple Lie subalgebra with an ideal, a theorem by Hochschild and Serre is used to characterize more precisely the cohomology of the gauge part of the BRST differential in the small algebra. In the case of an Abelian ideal, this leads to a complete solution of the Wess-Zumino consistency condition in this space. As an application, the consistent deformations of 2 + 1 dimensional Chern-Simons theory based on iso(2,1) are rediscussed. © 2002 American Institute of Physics.