Quantum BRST charge for quadratically nonlinear Lie algebras

Abstract

Quantum BRST charge for quadratically nonlinear lie algebras Schoutens, C.J.M.; Sevrin, A.; van Nieuwenhuizen, P. Published in: Communications in Mathematical Physics DOI:10.1007/BF01218470 Link to publicationCitation for published version (APA): Schoutens, K., Sevrin, A., & van Nieuwenhuizen, P. (1989). Quantum BRST charge for quadratically nonlinear lie algebras. Communications in Mathematical Physics, 124, 87-103. https://doi.org/10.1007/BF01218470 General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Download date: 01 May 2019Commun. Math. Phys. 124, 87-103 (1989) Abstract. We consider the construction of a nilpotent BRST charge for extensions of the Virasoro algebra of the form {Ta, Tb} =f,{Tc+ V~,~TcTd, (classical algebras in terms of Poisson brackets) and [To, TbJ = habI + f~{ T~ + V~ (T~ Te) (quantum algebras in terms of commutator brackets; normal ordering of the product (T~ Te) is understood). In both cases we assume that the set of generators {To} splits into a set {Hi} generating an ordinary Lie algebra and remaining generators {S,}, such that only the V~ 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 charge c = 100 and the so(N)-extended superconformal algebras with level S = -2(N -3).

Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space

“…The only difference of our case from [26] consists in the symmetry property of constants f km ij (35). In [26] …”

“…Moreover, there are no any guaranties that the commutator algebra is a Lie algebra. As we will see further, the algebra in the case under consideration is nonlinear and analogous to W 3 algebra (see e.g [26]). Besides, it turns out that some of the operators closing the algebra can not be interpreted as constraints.…”

“…Before we begin a construction of the BRST operator ones point out that the algebra of the enlarged operators in the case under consideration is very similar to one considered in [26].…”

“…At ξ i = 0 we have the symmetrized product of the operators in rhs of (60)-(62) and our algebra will be a partial case of the algebra considered in [26]. It was proved in [26] that the BRST operator includes the terms of first, thirds and seventh order in ghosts.…”

“…It was proved in [26] that the BRST operator includes the terms of first, thirds and seventh order in ghosts. Therefore one can expect in our case the analogous terms in BRST operator plus some extra terms stipulated by difference in symmetry of the constants f km ij .…”