Abstract
We consider the construction of a nilpotent BRST charge for extensions of the Virasoro algebra of the form {T a ,T b }=f c ab T c +V cd ab T c T d , (classical algebras in terms of Poisson brackets) and [T a ,T b ]=h ab I+f c ab T c +V cd ab (T c T d )(quantum algebras in terms of commutator brackets; normal ordering of the product (T c T d ) is understood). In both cases we assume that the set of generators {T a } splits into a set {H i } generating an ordinary Lie algebra and remaining generators {S α }, such that only theV αβ ij are nonvanishing. In the classical case a nilpotent BRST charge can always be constructed; for the quantum case we derive a condition which is necessary and sufficient for the existence of a nilpotent BRST charge. Non-trivial examples are the spin-3 algebra with central chargec=100 and theso(N)-extended superconformal algebras with levelS=−2(N−3).
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Communicated by L. Alvarez-Gaumé
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Schoutens, K., Sevrin, A. & van Nieuwenhuizen, P. Quantum BRST charge for quadratically nonlinear Lie algebras. Commun.Math. Phys. 124, 87–103 (1989). https://doi.org/10.1007/BF01218470
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DOI: https://doi.org/10.1007/BF01218470