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R. R. Metsaev

Publications and source records attributed to R. R. Metsaev.

At least 19 recordsLinked to original sources
arXiv2026

BRST-BV approach to fields in Poincare patch of AdS

We use the Poincare parametrization of AdS space to develop a general BRST-BV approach for free fields. A general expression for the BRST-BV Lagrangian of fields with arbitrary masses and symmetry types is obtained. We apply this general framework to study totally symmetric massless, massive, and partially-massless fields with arbitrary integer spin and a continuous-spin field. For these fields, the constrained and unconstrained BRST-BV formulations are developed. We investigate both irreducible and reducible fields. In addition, we demonstrate the matching between the obtained BRST-BV Lagrangian and the metric-like Lagrangian formulated in terms of the modified de Donder derivative. Finally, a realization of AdS space symmetries is obtained within the space of fields and antifields entering the BRST-BV formulation.

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arXiv2025

Lorentz covariant on-shell cubic vertices for continuous-spin fields and integer-spin fields

In the framework of Lorentz covariant on-shell approach, interacting continuous-spin fields and integer-spin fields in flat space are investigated. Continuous-spin fields are considered by using a Lorentz vector superspace formulation, while integer-spin fields are considered by using an oscillator formulation. All parity-even cubic vertices for self-interacting continuous-spin fields realized as functions on the Lorentz vector superspace are obtained. Cross-interactions of continuous-spin fields and integer-spin fields are also derived. Several representatives of cubic vertices realized as distributions are obtained. We show that manifestly Lorentz invariant formal cubic action involving at least one continuous-spin field turns out to be divergent. We find the modification of such action which maintains Lorentz invariance and leads to finite cubic action. One-to-one correspondence of Lorentz covariant cubic vertices and light-cone gauge cubic vertices is demonstrated explicitly.

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arXiv2025

Light-cone vector superspace and continuous-spin field in AdS

In the framework of light-cone gauge vector superspace, a continuous-spin field propagating in AdS space of dimension greater than or equal to four is studied. Use of such framework allows us to find a simple solution for spin operators entering our light-cone gauge Lagrangian formulation. Bosonic continuous-spin field is considered in AdS space of arbitrary dimensions, while the use of a helicity basis in four-dimensional AdS space allows us to consider bosonic and fermionic continuous-spin fields on an equal footing. Classification of continuous-spin fields is proposed. Conjectures on the notion of masslessness for continuous-spin field are made. All unitary irreps of non-linear spin algebra for four-dimensional AdS are also obtained.

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arXiv2025

Interacting massive/massless continuous-spin fields and integer-spin fields

In the framework of light-cone gauge approach, interacting continuous-spin fields and integer-spin fields propagating in flat space are studied. The continuous-spin fields are considered by using a light-cone gauge vector superspace formulation. Description of massive continuous-spin fields associated with the principal, complementary and discrete series is presented. For the massive continuous-spin fields of the principal and complementary series and massless continuous-spin fields, all parity-even cubic vertices realized as functions on the light-cone gauge vector superspace are obtained. Cubic vertices for a cross-interaction of massive/massless continuous spin fields and massive/massless integer-spin fields are also derived. These results for cubic vertices are complete for the dimensions of space-time greater than four. The use of the light-cone gauge vector superspace formulation considerably simplifies the cubic vertices as compared to the ones of oscillator formulation. Some cubic vertices realized as distributions are also found. Map between the oscillator formulation and the vector superspace formulation of the continuous-spin fields is explicitly described. An equivalence of the light-cone gauge and Lorentz covariant formulations of the free continuous-spin fields is also demonstrated.

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arXiv2024

Conformal Yang-Mills field in (A)dS space

Ordinary-derivative (second-derivative) Lagrangian formulation of classical conformal Yang-Mills field in the (A)dS space of six, eight, and ten dimensions is developed. For such conformal field, we develop two gauge invariant Lagrangian formulations which we refer to as generic formulation and decoupled formulation. In both formulations, the usual Yang-Mills field is accompanied by additional vector and scalar fields where the scalar fields are realized as Stueckelberg fields. In the generic formulation, the usual Yang-Mills field is realized as a primary field, while the additional vector fields are realized as auxiliary fields. In the decoupled formulation, the usual Yang-Mills field is realized as massless field, while the additional vector fields together with the Stueckelberg are realized as massive fields. Some massless/massive fields appear with the wrong sign of kinetic terms, hence demonstrating explicitly that the considered models are not unitary. The use of embedding space method allows us to treat the isometry symmetries of (A)dS space manifestly and obtain conformal transformations of fields in a relatively straightforward way. By accompanying each vector field by the respective gauge parameter, we introduce an extended gauge algebra. Levy-Maltsev decomposition of such algebra is noted. Use of the extended gauge algebra setup allows us to present concise form for the Lagrangian and gauge transformations of the conformal Yang-Mills field. Higher-derivative representation of the Lagrangian is also obtained.

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arXiv2023

Conformal Yang-Mills field in arbitrary dimensions

Lagrangian of a classical conformal Yang-Mills field in the flat space of even dimension greater than or equal to six involves higher derivatives. We study Lagrangian formulation of the classical conformal Yang-Mills field by using ordinary-derivative (second-derivative) approach. In the framework of the ordinary-derivative approach, a field content, in addition to generic Yang-Mills field, consists of auxiliary vector fields and Stueckelberg scalar fields. For such field content, we obtain a gauge invariant Lagrangian with the conventional second-derivative kinetic terms and the corresponding gauge transformations. The Lagrangian is built in terms of non-abelian field strengths. Structure of a gauge algebra entering gauge symmetries of the conformal Yang-Mills field is described. FFF-vertex of the conformal Yang-Mills field which involves three derivatives is also obtained. For six, eight, and ten dimensions, eliminating the auxiliary vector fields and gauging away the Stueckelberg scalar fields, we obtain a higher-derivative Lagrangian of the conformal Yang-Mills field. For arbitrary dimensions, we demonstrate that all auxiliary fields can be integrated out at non-linear level leading just to a local higher-derivative action which is expressed only in terms of the generic Yang-Mills field.

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arXiv2023

Light-cone gauge massive and partially-massless fields in AdS(4)

Using light-cone gauge approach, bosonic and fermionic massive and partially-massless fields in AdS(4) space are considered. For such fields, light-cone gauge action is presented. Considering the massive and partially-massless fields in helicity basis and CFT adapted basis, two simple representations of spin operators entering the light-cone gauge action are discussed. The simple representations for the spin operators are obtained by using bosonic spinor-like oscillators. The bosonic spinor-like oscillators allow also us to treat the bosonic and fermionic fields on an equal footing.

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arXiv2022

Interacting massive and massless arbitrary spin fields in 4d flat space

Massive and massless arbitrary integer spin fields propagating in four-dimensional flat space are studied. The massive and massless fields are treated by using a light-cone gauge helicity basis formalism. Cubic cross-interactions between massive and massless fields and cubic interactions between massive fields are investigated. We introduce a classification of such cubic interactions and using our classification we build all cubic interaction vertices. Realization of generators of the Poincare algebra on space of interacting fields is found. As a by-product, some illustrative examples of light-cone form for 3-point invariant amplitudes of massive and massless fields are also discussed.

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arXiv2022

General light-cone gauge approach to conformal fields and applications to scalar and vector fields

Totally symmetric arbitrary spin conformal fields propagating in the flat space of even dimension greater than or equal to four are studied. For such fields, we develop a general ordinary-derivative light-cone gauge formalism and obtain restrictions imposed by the conformal algebra symmetries on interaction vertices. We apply our formalism for the detailed study of conformal scalar and vector fields. For such fields, all parity-even cubic interaction vertices are obtained. The cubic vertices obtained are presented in terms of dressing operators and undressed vertices. We show that the undressed vertices of the conformal scalar and vector fields are equal, up to overall factor, to the cubic vertices of massless scalar and vector fields. Various conjectures about interrelations between the cubic vertices for conformal fields in conformal invariant theories and the cubic vertices for massless fields in Poincare invariant theories are proposed.

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arXiv2022

Mixed-symmetry continuous-spin fields in flat and AdS spaces

In the framework of light-cone gauge approach, bosonic and fermionic mixed-symmetry continuous-spin fields in AdS space and flat space are considered. For such fields, the light-cone gauge actions are found. Realization of relativistic symmetries of AdS and flat spaces on the continuous-spin fields is also presented. Simple realization of spin operators is found. With respect to vector variable entering the continuous-spin fields, the spin operators for the fields in flat space turn out to be first-order differential operators, while, for the the fields in AdS space, the spin operators are realized as the second-order differential operators. By product, we obtain also the simple description of triplectic mixed-symmetry continuous-spin fields.

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arXiv2021

Superfield approach to interacting N=2 massive and massless supermultiplets in 3d flat space

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 generators of the N=2 Poincare superalgebra is also found.

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arXiv2020

Conformal totally symmetric arbitrary spin fermionic fields

Conformal totally symmetric arbitrary spin fermionic fields propagating in the flat space-time of even dimension greater than or equal to four are investigated. First-derivative metric-like formulation involving Fang-Fronsdal kinetic operator for such fields is developed. Gauge invariant Lagrangian and the corresponding gauge transformations are obtained. Gauge symmetries of the Lagrangian are realized by using auxiliary fields and the Stueckelberg fields. Realization of conformal algebra symmetries on the space of conformal gauge fermionic fields is obtained. The on-shell degrees of freedom of the fermionic arbitrary spin conformal fields are also studied.

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arXiv2020

Cubic interactions of arbitrary spin fields in 3d flat space

Using light-cone gauge formulation, massive arbitrary spin irreducible fields and massless (scalar and one-half spin) fields in three-dimensional flat space are considered. Both the integer spin and half-integer spin fields are studied. For such fields, we provide classification for cubic interactions and obtain explicit expressions for all cubic interaction vertices. We study two forms of the cubic interaction vertices which we refer to as first-derivative form and higher-derivative form. All cubic interaction vertices are built by using the first-derivative form.

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arXiv2019

Cubic interactions for arbitrary spin N-extended massless supermultiplets in 4d flat space

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 vertices. Superspace realization of relativistic symmetries of the N-extended Poincare superalgebra on space of interacting fields is also obtained.

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arXiv2019

Cubic interaction vertices for N=1 arbitrary spin massless supermultiplets in flat space

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 superalgebra on space of interacting superfields is also found.

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arXiv2019

Light-cone continuous-spin field in AdS space

We develop further the general light-cone gauge approach in AdS space and apply it for studying continuous-spin field. For such field, we find light-cone gauge Lagrangian and realization of relativistic symmetries. We find a simple realization of spin operators entering our approach. Generalization of our results to the gauge invariant Lagrangian formulation is also described. We conjecture that, in the framework of AdS/CFT, the continuous-spin AdS field is dual to light-ray conformal operator. For some particular cases, our continuous-spin field leads to reducible models. We note two reducible models. The first model consists of massive scalar, massless vector, and partial continuous-spin field involving fields of all spins greater than one, while the second model consists of massive vector, massless spin-2 field, and partial continuous-spin field involving all fields of spins greater than two.

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arXiv2018

Cubic interaction vertices for massive/massless continuous-spin fields and arbitrary spin fields

We use light-cone gauge formalism to study interacting massive and massless continuous-spin fields and finite component arbitrary spin fields propagating in the flat space. Cubic interaction vertices for such fields are considered. We obtain parity invariant cubic vertices for coupling of one continuous-spin field to two arbitrary spin fields and cubic vertices for coupling of two continuous-spin fields to one arbitrary spin field. Parity invariant cubic vertices for self-interacting massive/massless continuous-spin fields are also obtained. We find the complete list of parity invariant cubic vertices for continuous-spin fields and arbitrary spin fields.

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