We develop a general gauge-invariant Lagrangian construction for half-integer higher spin fields in the AdS space of any dimension. Starting with a formulation in terms of an auxiliary Fock space, we obtain closed nonlinear symmetry algebras of higher spin fermionic fields in the AdS space and find the corresponding BRST operator. A universal procedure for constructing gauge-invariant Lagrangians describing the dynamics of fermionic fields of any spin is developed. No off-shell constraints for the fields and gauge parameters are imposed from the very beginning. It is shown that all the constraints determining an irreducible representation of the AdS group arise as a consequence of the equations of motion and gauge transformations. As an example of the general procedure, we derive gauge-invariant Lagrangians for massive fermionic fields of spin 1/2 and 3/2 containing the complete set of auxiliary fields and gauge symmetries.

Lagrangian quantization rules for general gauge theories are proposed on a basis of a superfield formulation of the standard BRST symmetry. Independence of the S-matrix on a choice of the gauge is proved. The Ward identities in terms of superfields are derived.

A definition of soft breaking of BRST symmetry in the field-antifield formalism is proposed, valid for general gauge theories and arbitrary gauge fixing. The Ward identities for the generating functionals of Green's functions are derived, and their gauge dependence is investigated. We discuss the Gribov-Zwanziger action for the one-parameter family of R ξ gauges. It is argued that gauge theories with a soft breaking of BRST symmetry are inconsistent.

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.

We introduce the notion of finite BRST-antiBRST transformations, both global and field-dependent, with a doublet λ a , a = 1, 2, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in Yang-Mills theories. It turns out that the finite transformations are quadratic in their parameters. At the same time, exactly as in the case of finite field-dependent BRST transformations for the Yang-Mills vacuum functional, special field-dependent BRST-antiBRST transformations, with s a -potential parameters λ a = s a Λ induced by a finite even-valued functional Λ and by the anticommuting generators s a of BRST-antiBRST transformations, amount to a precise change of the gaugefixing functional. This proves the independence of the vacuum functional under such BRST-antiBRST transformations. We present the form of transformation parameters that generates a change of the gauge in the path integral and evaluate it explicitly for connecting two arbitrary R ξ -like gauges. For arbitrary differentiable gauges, the finite field-dependent BRST-antiBRST transformations are used to generalize the Gribov horizon functional h, given in the Landau gauge, and being an additive extension of the YangMills action by the Gribov horizon functional in the Gribov-Zwanziger model. This generalization is achieved in a manner consistent with the study of gauge independence. We also discuss an extension of finite BRST-antiBRST transformations to the case of general gauge theories and present an ansatz for such transformations.

We continue the study of finite BRST-antiBRST transformations for general gauge theories in Lagrangian formalism initiated in [1], with a doublet λ a , a = 1, 2, of anticommuting Grassmann parameters, and find an explicit Jacobian corresponding to this change of variables for constant λ a . This makes it possible to derive the Ward identities and their consequences for the generating functional of Green's functions. We announce the form of the Jacobian (proved to be correct in [31]) for finite field-dependent BRSTantiBRST transformations with functionally-dependent parameters, λ a = s a Λ, induced by a finite evenvalued functional Λ(φ, π , λ) and by the generators s a of BRST-antiBRST transformations, acting in the space of fields φ, antifields φ * a , φ and auxiliary variables π a , λ. On the basis of this Jacobian, we present and solve a compensation equation for Λ, which is used to achieve a precise change of the gauge-fixing functional for an arbitrary gauge theory. We derive a new form of the Ward identities, containing the parameters λ a , and study the problem of gauge-dependence. The general approach is exemplified by the Freedman-Townsend model of a non-Abelian antisymmetric tensor field.

We continue our study of finite BRST-anti-BRST transformations for general gauge theories in Lagrangian formalism, initiated in [arXiv:1405.0790 [hep-th] and arXiv:1406.0179 [hep-th]], with a doublet λa, a = 1, 2, of anticommuting Grassmann parameters, and prove the correctness of the explicit Jacobian in the partition function announced in [arXiv:1406.0179 [hep-th]], which corresponds to a change of variables with functionally dependent parameters λa = UaΛ induced by a finite Bosonic functional Λ(φ, π, λ) and by the anticommuting generators Ua of BRST-anti-BRST transformations in the space of fields φ and auxiliary variables π a , λ. We obtain a Ward identity depending on the field-dependent parameters λa and study the problem of gauge dependence, including the case of Yang-Mills theories. We examine a formulation with BRST-anti-BRST symmetry breaking terms, additively introduced into the quantum action constructed by the Sp(2)-covariant Lagrangian rules, obtain the Ward identity and investigate the gauge independence of the corresponding generating functional of Green's functions. A formulation with BRST symmetry breaking terms is developed. It is argued that the gauge independence of the above generating functionals is fulfilled in the BRST and BRST-anti-BRST settings. These concepts are applied to the average effective action in Yang-Mills theories within the functional renormalization group approach.

We construct a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with the corresponding Young tableaux having two rows, on a basis of the BRST approach. Starting with a description of fermionic higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space, 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 auxiliary representations of the constraint subsuperalgebra containing the subsystem of second-class constraints in terms of Verma modules. We propose a universal procedure of constructing gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of both massless and massive fermionic fields of any spin. No off-shell constraints for the fields and gauge parameters are used from the very beginning. 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. To illustrate the general construction, we obtain a Lagrangian description of fermionic fields with generalized spin (3/2,1/2) and (3/2,3/2) on a flat background containing the complete set of auxiliary fields and gauge symmetries. * Ramond-Ramond background [29,30] and the conformal N = 4 SYM theory in the context of the AdS/CFT correspondence [31].At present, the dynamics of totally symmetric higher-spin fields presents the most developed direction in the variety of unitary representations of the Poincare and AdS algebras [2,3,16,17,21]. To a great extent, this is caused by the fact that in a 4d space-time there is no place for mixedsymmetry irreducible representations with the exception of dual theories 1 . In higher space-time dimensions, there appear mixed-symmetry representations determined by more than one spinlike parameters, and the problem of their field-theoretic description is not so well-developed as for totally symmetric irreps. Starting from the papers of Fierz-Pauli and Singh-Hagen [1, 2] for higher-spin field theories in the Minkowski space, it has been known that all such theories include, together with the basic fields of a given spin, also some auxiliary fields of lower spins, necessary to provide a compatibility of the Lagrangian equations of motion with the relations that determine irreducible representations of the Poincare group. Attempts to construct Lagrangian descriptions of free and interacting higher-spin field theories have resulted in consistency problems, which are not completely resolved until now.The present work is devoted to the construction of gauge-invariant Lagrangians for both massless and massive mixed-symmetry spin-tensor fields of rank n 1 + n 2 + ... + n k , with any integer numbers n 1 ≥ n 2 ≥ ... ≥ n k ≥ 1 for k = 2 in a d-dimensional Minkowski space, the fields being elements of Poincare-group irreps with a Young tableaux...