我们将先前在[Nucl.Phys. B 779（2007）155]中开发的自由无质量高自旋场的无约束描述推广到任意维平坦空间中自由有质量高自旋场的情况。对于任意自旋值，拉格朗日量以易于处理的形式给出。它是本地的，从更高的衍生条款，并涉及到一个自由的质量更高的自旋场在任意维的无约束规范不变描述所需的辅助领域的最小数量。
英文摘要：
We generalize the unconstrained description of free massless higher spin fields previously developed in [Nucl.Phys. B 779 (2007) 155] to the case of free massive higher spin fields in a flat space of arbitrary dimension. The Lagrangian is given in an easy-to-handle form for an arbitrary value of spin. It is local, free from higher derivative terms, and involves a minimal number of auxiliary fields needed for an unconstrained gauge invariant description of a free massive higher spin field in arbitrary dimension.
New method (arXiv:2104.11930) is applied to construct cubic interactions of massless spin 4 and real scalar fields. In contrast with the case of massless spin 3 fields (arXiv:2208.05700, 2209.03678, 2210.02842) the procedure requires to use an unconstrained formulation (arXiv:0702.161) for the Fronsdal theory. It is shown that in the unconstrained formulation there exists a four-parameter family of cubic interactions between massless spin 4 and real scalar fields, which contains four derivatives in vertices and is invariant with respect to the original gauge transformation. These vertices cont…
We consider unconstrained formulation of the higher spin gauge theory in anti de Sitter (AdS) spacetime, given by actions [1, 2], and provide on-shell supersymmetry transformations for the $\mathcal{N}=1$ unconstrained massless higher spin supermultiplet in four-dimensional AdS$_4$. Such an irreducible supermultiplet $(Φ_1, Φ_2 \,; Ψ_1,Ψ_2)$ contains a pair of bosonic fields, with opposite parity, which are generating functions (infinite collection of totally symmetric real tensor fields of all integer rank $s= 0, 1, \ldots, \infty$), as well as two fermionic fields, which have opposite signs …
The unconstrained frame-like formulation of an infinite tower of completely symmetric tensor gauge fields is reviewed and examined in the limit where the cosmological constant goes to zero. By partially fixing the gauge and solving the torsion constraints, the form of the gauge transformations in the unconstrained metric-like formulation are obtained till first order in a weak field expansion. The algebra of the corresponding gauge symmetries is shown to be equivalent, at this order and modulo (unphysical) gauge parameter redefinitions, to the Lie algebra of Hermitian differential operators on…
The local free action principle for bosonic unconstrained higher spin gauge fields in $d$-dimensional (A)dS$_d$ spacetime has been already established by Segal. However, later on, Schuster and Toro, in 4-dimensional flat spacetime, extracted such an action from their bosonic continuous spin gauge theory, when the continuous spin parameter vanishes. On the other hand, similar to the Schuster-Toro's action, we found the fermionic continuous spin gauge theory in 4-dimensional flat spacetime. Thus it is noteworthy to take out its fermionic higher spin formulation in a limit, and generalize it to $…
We provide a review of gauge field theories with higher spin, focusing on the classical theory of massless bosons in flat Minkowski spacetime. A brief introduction to the concept of spin is provided along with a historical review of some of the most important problems and accomplishments in higher spin theory, followed by a review of familiar lower spin theories. Using a particularly elegant formalism, we examine the free higher spin theory and the theory coupled to a generic external current. For both of these theories, we review their constrained and the unconstrained formulation, focusing o…
We investigate the unfolded formulation of bosonic Lorentz tensor fields of arbitrary spin in $AdS_3$ containing a parity breaking mass parameter. They include deformations of the linearisations of the Prokushkin--Vasiliev higher spin theory around its critical points. They also provide unfolded formulations of linearized topologically massive higher spin fields including their critical versions. The gauge invariant degrees of freedom are captured by infinite towers of zero forms. We also introduce two inequivalent sets of gauge potentials given by trace constrained Fronsdal fields and trace u…
N-extended massless arbitrary integer and half-integer spin supermultiplets in four dimensional flat space are studied in the framework of light-cone gauge formalism. For such multiplets, by using light-cone momentum superspace, we build unconstrained light-cone gauge superfield formulation. The superfield formulation is used to develop a superspace representation for all cubic interactions vertices of the N-extended massless supermultiplets. Our suitable treatment of the light-cone gauge superfields allows us to obtain attractively simple superspace representation for the cubic interaction ve…
BRST-BFV method for constrained Lagrangian formulations (LFs) for (ir)reducible half-integer HS Poincare group representations in Minkowski space is suggested. The procedure is derived by 2 ways: from the unconstrained BRST-BFV method for mixed-symmetry HS fermionic fields subject to an arbitrary Young tableaux with k rows (suggested in arXiv:1211.1273[hep-th]) by extracting the second-class constraints, $\widehat{O}_α=(\widehat{O}_a, \widehat{O}^+_a)$, from a total superalgebra of constraints, second, in self-consistent way by means of finding BRST-extended initial off-shell algebraic constra…
Taking into account the Schuster-Toro action and its fermionic analogue discovered by us, we supersymmetrize unconstrained formulation of the continuous spin gauge field theory. Afterwards, building on the Metsaev actions, we supersymmetrize constrained formulation of the theory. In each formulation, we provide supersymmetry transformations for the $\mathcal{N}=1$ supermultiplet in four-dimensional flat space-time, in which continuous spin particle (CSP) is considered to be a complex scalar continuous spin field, and its superpartner which can be called ``\,CSPino\,'' is considered to be a Dir…
In the framework of light-cone gauge formulation, massless arbitrary spin N=1 supermultiplets in four-dimensional flat space are considered. We study both the integer (super)spin and half-integer (super)spin supermultiplets. For such supermultiplets, formulation in terms of unconstrained light-cone gauge superfields defined on chiral momentum superspace is used. Superfield representation for all cubic interaction vertices of the supermultiplets is obtained. Representation of the cubic vertices in terms of component fields is derived. Realization of relativistic symmetries of N=1 Poincare super…
Gauge invariant Lagrangian descriptions of irreducible and reducible half-integer higher-spin mixed-symmetric massless and massive representations of the Poincare group with off-shell algebraic constraints are constructed within a metric-like formulation in a $d$-dimensional flat space-time on the basis of a suggested constrained BRST approach. A Lorentz-invariant resolution of the BRST complex within the constrained BRST formulations produces a gauge-invariant Fang-Fronsdal Lagrangian entirely in terms of the initial triple gamma-traceless spin-tensor field $Ψ_{(μ)_{n}}$ with gamma-traceless …
Massive arbitrary spin supermultiplets and massless (scalar and spin one-half) supermultiplets of the N=2 Poincare superalgebra in three-dimensional flat space are considered. Both the integer spin and half-integer spin supermultiplets are studied. For such massive and massless supermultiplets, a formulation in terms of light-cone gauge unconstrained superfields defined in a momentum superspace is developed. For the supermultiplets under consideration a superspace first derivative representation for all cubic interaction vertices is obtained. A superspace representation for dynamical generator…
In massive gravity and bigravity, spin-2 interactions are defined in terms of a square root matrix that involves two metrics. In this work, the interactions are constructed using a congruence matrix between the metrics. It is established that the primary square root matrix function is the only power series solution to the equations of motion for the congruence. Moreover, the shift vector redefinition that is used in the bimetric ghost-free proofs follows from the $N+1$ form of the equations of motion. The analysis also gives an insight into the vielbein formulation of spin-2 interactions since…
Gauge-invariant descriptions for a free bosonic scalar field of continuous spin in a $d$-dimensional Minkowski space-time using a metric-like formulation are constructed on the basis of a constrained BRST-BFV approach we propose. The resulting BRST-BFV equations of motion for a scalar field augmented by ghost operators contains different sets of auxiliary fields, depending on the manner of a partial gauge-fixing and a resolution of some of the equations of motion for a BRST-unfolded first-stage reducible gauge theory. To achieve an equivalence of the resulting BRST-unfolded constrained equatio…
The details of unconstrained Lagrangian formulations (being continuation of earlier developed research for Bose particles in NPB 862 (2012) 270, [arXiv:1110.5044[hep-th]], Phys. of Part. and Nucl. 43 (2012) 689, [arXiv:1202.4710 [hep-th]]) are reviewed for Fermi particles propagated on an arbitrary dimensional Minkowski space-time and described by the unitary irreducible half-integer higher-spin representations of the Poincare group subject to Young tableaux $Y(s_1,...,s_k)$ with $k$ rows. The procedure is based on the construction of the Verma modules and finding auxiliary oscillator realizat…
