Frame-like Actions for Massless Mixed-Symmetry Fields in Minkowski space. Fermions

We construct a Lagrangian description of irreducible integer higher-spin representations of the Poincare group with an arbitrary Young tableaux having k rows, on a basis of the universal BRST approach. Starting with a description of bosonic mixed-symmetry higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space associated with special Poincare module, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a first-class constraint system. For this purpose, we find, for the first time, auxiliary representations of the constraint subalgebra, to be isomorphic due to Howe duality to sp(2k) algebra, and containing the subsystem of second-class constraints in terms of new oscillator variables. We propose a universal procedure of constructing unconstrained gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of both massless and massive bosonic fields of any spin. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by the constraints corresponding to an irreducible Poincare-group representation. As examples of the general procedure, we formulate the method of Lagrangian construction for bosonic fields subject to arbitrary Young tableaux having 3 rows and derive the gaugeinvariant Lagrangian for new model of massless rank-4 tensor field with spin (2, 1, 1) and second-stage reducible gauge symmetries.

Section: Introductionmentioning

confidence: 99%

General Lagrangian formulation for higher spin fields with arbitrary index symmetry. I. Bosonic fields

Buchbinder

Reshetnyak

2012

“…In this and the following subsections we use the results of [19] (see also [33,34]) which provided the generalization of the bosonic formalism [25] to the fermionic case.…”

Section: Mixed Symmetry Spin-tensormentioning

confidence: 99%

Infinite (continuous) spin fields in the frame-like formalism

Khabarov

Zinoviev

2018

In this paper we elaborate on the gauge invariant frame-like Lagrangian description for the wide class of the so-called infinite (or continuous) spin representations of Poincaré group. We use our previous results on the gauge invariant formalism for the massive mixed symmetry fields corresponding to the Young tableau with two rows Y (k, l) (Y (k +1/2, l+1/2) for the fermionic case). We have shown that the corresponding infinite spin solutions can be constructed as a limit where k goes to infinity, while l remain to be fixed and label different representations. Moreover, our gauge invariant formalism provides a natural generalization to (Anti) de Sitter spaces as well. As in the completely symmetric case considered earlier by Metsaev we have found that there are no unitary solutions in de Sitter space, while there exists a rather wide spectrum of Anti de Sitter ones. In this, the question what representations of the Anti de Sitter group such solutions correspond to remains to be open.

“…As a result, all degrees of freedom in the gauge parameters |Λ (2)0 g0 (2,1) , |Λ (2)1 0 (2,1) are used, and the theory becomes a first-stage-reducible gauge theory with the independent parameter |Λ (1)l g0 (2,1) , l = 0, 1, in which only the component spin-tensors ψ (1)1 r , for r = 1 − 4, 6, 7, 9, ψ (1)1 t|µ , for t = 5, 8 and ψ (1)0 m|µν , ψ ′(1)0 n|µ , ψ (1)0 u|µ , ψ (1)0 v , for m = 13, 18; n = 1, 6; u = 1, 6, 9, 10, 14, 15, 21; r = 13, 18; v = 1 − 8, 11, 12, 16, 17, 19 − 21 survive. For the reducible gauge parameters |Λ l 0 (2,1) , l = 0, 1 determined by Eqs. (D.10)-(D.13) the general gauge conditions (C.12), having the form (for s max = 3) 6,11,17,18,20,23,28,29,34,35; ψ 0 t|µ , for t = 20, 23, 35; ψ 0 35|µν . (6.47)…”

Section: Reducible Gauge Transformations For Gauge Parametersmentioning

confidence: 99%

General Lagrangian formulation for higher spin fields with arbitrary index symmetry. 2. Fermionic fields

Reshetnyak

2013

We continue the construction of a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with an arbitrary Young tableaux having k rows, on a basis of the BRST-BFV approach suggested for bosonic fields in our first article (Nucl. Phys. B862 (2012) 270, [arXiv:1110). Starting from a description of fermionic mixed-symmetry higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space associated with a special Poincare module, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a system of first-class constraints. To do this, we find, in first time, by means of generalized Verma module the auxiliary representations of the constraint subsuperalgebra, to be isomorphic due to Howe duality to osp(1|2k) superalgebra, and containing the subsystem of second-class constraints in terms of new oscillator variables. We suggest a universal procedure of finding unconstrained gauge-invariant Lagrangians with reducible gauge symmetries, describing the dynamics of both massless and massive fermionic fields of any spin. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by constraints corresponding to an irreducible Poincare-group representation. As examples of the general approach, we propose a method of Lagrangian construction for fermionic fields subject to an arbitrary Young tableaux having 3 rows, and obtain a gauge-invariant Lagrangian for a new model of a massless rank-3 spintensor field of spin (5/2, 3/2) with first-stage reducible gauge symmetries and a non-gauge Lagrangian for a massive rank-3 spin-tensor field of spin (5/2, 3/2). and fermionic fields of various spins, providing the consideration of higher-spin theory as a tool of investigating the structure of superstring theory. For the current progress in higher-spin field theory, see the reviews [1], whereas some recent directions in higher-spin theory, starting from the pioneering papers [2], [3], [4], are examined in [5]- [20].The dynamics of totally symmetric free higher-spin fields is currently the most well-developed area in the variety of unitary representations of the Poincare and AdS algebras [3], [4], [21], [22]. This situation is due to the fact that a 4d space-time does not admit any mixed-symmetry irreducible representations, except for dual theories. It is well-known that in higher space-time dimensions there arise mixed-symmetry representations, determined by spin-like parameters being more than one in number [23], [24], [25], whereas their field-theoretic description is not so well-developed as for totally symmetric representations. While the simplest mixed-symmetric HS bosonic fields were examined in [26], attempts to construct Lagrangian descriptions of free and interacting higher-spin field theories have met with consistency problems, which have not yet been completely solved. Unconstrained Lagrangians for half-integer H...