Higher order BRST and anti-BRST operators and cohomology for compact Lie algebras

C. Chryssomalakos; J. A. de Azcarraga; A. J. Macfarlane; J. C. Perez Bueno

doi:10.1063/1.533067

paper

Higher order BRST and anti-BRST operators and cohomology for compact Lie algebras

arXiv:hep-th/9810212 · doi:10.1063/1.533067

Abstract

After defining cohomologically higher order BRST and anti-BRST operators for a compact simple algebra {\cal G}, the associated higher order Laplacians are introduced and the corresponding supersymmetry algebra $Σ$ is analysed. These operators act on the states generated by a set of fermionic ghost fields transforming under the adjoint representation. In contrast with the standard case, for which the Laplacian is given by the quadratic Casimir, the higher order Laplacians $W$ are not in general given completely in terms of the Casimir-Racah operators, and may involve the ghost number operator. The higher order version of the Hodge decomposition is exhibited. The example of su(3) is worked out in detail, including the expression of its higher order Laplacian W.

31 pages, two figures, latex2e file. Replacement (May 14, 1999): a comment and references added. To appear in JMP