Towards Lagrangian formulations of mixed-symmetry higher spin fields on AdS-space within BFV-BRST formalism
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ESSION “QUANTUM FIELD THEORY AND THEORY OF ELEMENTARY PARTICLES”
Towards Lagrangian Formulations of MixedSymmetry Higher Spin Fields on AdSSpace within BFVBRST Formalism1, 2 A. A. Reshetnyak Institute of Strength Physics and Materials Science, 634021, Tomsk, Russia Abstract—The spectrum of superstring theory on the AdS5 × S5 RamondRamond background in tensionless limit contains integer and halfinteger higherspin fields subject at most to tworows Young tableaux Y(s1, s2). We review the details of a gaugeinvariant Lagrangian description of such massive and massless higherspin fields in antideSitter spaces with arbitrary dimensions. The procedure is based on the construction of Verma modules, its oscillator realizations and of a BFVBRST operator for nonlinear algebras encoding unitary irreducible representations of AdS group. DOI: 10.1134/S1063779610060341 21
1. INTRODUCTION
Launch of LHC on the rated capacity assumes not only the answer on the question on existence of Higgs boson, the proof of supersymmetry display and a new insight on origin of Dark Matter, but permits one to reconsider the problems of an unique description of variety of elementary particles and all known interac tions. In this relation, the development of higherspin (HS) field theory in view of its close relation to super string theory on constant curvature spaces, which operates with an infinite set of massive and massless bosonic and fermionic HS fields subject to multirow Young tableaux (YT) Y(s1, …, sk), k ≥ 1 (see for a review, [1]) seems by actual one. The paper considers the last results of constructing Lagrangian formula tions (LFs) for free integer and halfinteger HS fields on AdSdspace with Y(s1, s2) in Fronsdal metriclike formalism within BFVBRST approach [2] as a start ing point for an interacting HS field theory in the framework of conventional Quantum Field Theory, and in part based on the results presented in [3–6]. This method of Lorentzcovariant constructing LF for HS fields, developed originally in a way that applies to Hamiltonian quantization of gauge theories with a given LF, consists in a solution of the problem inverse to that of the method [2] (as in the case of string field theory [7]) in the sense of constructing a classical gauge LF with respect to a nilpotent BFVBRST oper ator Q. In detail, the solution of inverse problem includes 4 steps: —the realization of initial irrep conditions of AdS group, that extract the fields with a definite mass m and 1 Talk
on the International Bogolyubov Conference2009 “Prob lems of Theoretical and Mathematical Physics,” Moscow– Dubna, August 21–27, 2009. 2 The article is published in the original.
generalized spin s = (s1, …, sk) [8] as operator mixed class constraints oI in a special Fock space ; —the additive conversion (following to [9]) of algebra oI into one of OI: OI = oI + o 'I , [oI, o 'J } = 0, determined on wider Fock space, ⊗ ' with only firstclass constraints Oα ⊂ OI; —the construction of the Hermitian nilpotent BFVBRST operator Q' for non
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