BRST-BV quantum actions for constrained totally-symmetric integer HS fields

Burdı́k, Č.; Reshetnyak, Alexander A.

doi:10.1016/j.nuclphysb.2021.115357

Cited by 8 publications

(5 citation statements)

References 59 publications

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“…The suggested approach can be further developed: for irreducible massless half-integer higher-spin fields on a flat background; for massive integer and half-integer higher-spin fields; for higher-spin fields of a mixed index symmetry; for supersymmetric fields of higher spins, where the vertices must include any degree of traces. One should also mention the problem of constructing the quartic and higher vertices in the BRST approach, as well as the quantization of a model of interacting higher-spin fields, by following the algorithm for constructing a quantum BRST-BV action [23]. All the mentioned problems are awaiting their solution in our forthcoming works.…”

Section: Discussionmentioning

confidence: 99%

Towards the structure of a cubic interaction vertex for massless integer higher spin fields

Reshetnyak

2022

Preprint

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The structure of a cubic Lagrangian vertex is clarified for irreducible fields of helicities s 1 , s 2 , s 3 in a d-dimensional Minkowski space. An explicit form of the operator Z j entering the vertex in a non-multiplicative way (examined in [6] for j = 1) is obtained. The solution is found within the BRST approach with complete BRST operators, which contain all constraints corresponding to the conditions that extract the irreducible fields, including trace operators.

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Section: Discussionmentioning

confidence: 99%

Towards the structure of a cubic interaction vertex for massless integer higher spin fields

Reshetnyak

2022

Preprint

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“…We stress, that there are no terms in any obtained interacting vertices, and therefore, in the interacting part of the action with divergences by construction. It means that on mass-shell after gauge-fixing determined by the Lorentz-like or (in general, R ξ -type, see e.g., [58]) gauge to derive the non-degenerate quantum action for the interacting model in question the vertices do not vanish.…”

Section: Discussionmentioning

confidence: 99%

“…One should also note the problems of constructing the fourth and higher vertices and related various problems of locality (see the discussion initiated in [68], then in [69][70][71] with recent analysis [72] and also [73][74][75][76]), where the BRST approach can possibly be useful. The construction and quantum loop calculations with the BRST quantum action for the models with derived cubic vertices can be realized within the BRST approach following to [58]. We plan to address all of the mentioned problems in the forthcoming works.…”

Section: Discussionmentioning

confidence: 99%

Covariant Cubic Interacting Vertices for Massless and Massive Integer Higher Spin Fields

Buchbinder,

Reshetnyak

2023

Symmetry

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We develop the BRST approach to construct the general off-shell local Lorentz covariant cubic interaction vertices for irreducible massless and massive higher spin fields on d-dimensional Minkowski space. We consider two different cases for interacting higher spin fields: with one massive and two massless; two massive, both with coinciding and with different masses and one massless field of spins s1,s2,s3. Unlike the previous results on cubic vertices we extend our earlier result in (Buchbinder, I.L.; et al. Phys. Lett. B 2021, 820, 136470) for massless fields and employ the complete BRST operator, including the trace constraints, which is used to formulate an irreducible representation with definite integer spin. We generalize the cubic vertices proposed for reducible higher spin fields in (Metsaev, R.R. Phys. Lett. B 2013, 720, 237) in the form of multiplicative and non-multiplicative BRST-closed constituents and calculate the new contributions to the vertex, which contains the additional terms with a smaller number of space-time derivatives. We prove that without traceless conditions for the cubic vertices in (Metsaev, R.R. Phys. Lett. B 2013, 720, 237) it is impossible to provide the noncontradictory Lagrangian dynamics and find explicit traceless solution for these vertices. As the examples, we explicitly construct the interacting Lagrangians for the massive spin of the s field and the massless scalars, both with and without auxiliary fields. The interacting models with different combinations of triples higher spin fields: massive spin s with massless scalar and vector fields and with two vector fields; massless helicity λ with massless scalar and massive vector fields; two massive fields of spins s, 0 and massless scalar is also considered.

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“…We expect, first of all, to use the deformation procedure for irreducible totally symmetric massless HS fields elaborated for free fields in [37] as applied to AdS spaces, and also anticipate the concept of BRST-BV quantization as applied to deduce interacting models in the BRST approach, while adapting the algorithm developed in flat spaces [110], albeit with a complete BRST operator, as in the case of a minimal BRST-BV action [111]. As a subsquent problem to be solved, we intend to apply our results to an explicit construction of a generalized Verma module, a BRST operator, and an LF for irreducible massive half-integer HS fields of spin (n 1 + 1/2, n 2 + 1/2) subject to Y(n 1 , n 2 ) in AdS spaces.…”

Section: Discussionmentioning

confidence: 99%

Gauge-Invariant Lagrangian Formulations for Mixed-Symmetry Higher-Spin Bosonic Fields in AdS Spaces

Reshetnyak,

Moshin

2023

Universe

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We deduce a non-linear commutator higher-spin (HS) symmetry algebra which encodes unitary irreducible representations of the AdS group—subject to a Young tableaux Y(s1,…,sk) with k≥2 rows—in a d-dimensional anti-de Sitter space. Auxiliary representations for a deformed non-linear HS symmetry algebra in terms of a generalized Verma module, as applied to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints, are found explicitly in the case of a k=2 Young tableaux. An oscillator realization over the Heisenberg algebra for the Verma module is constructed. The results generalize the method of constructing auxiliary representations for the symplectic sp(2k) algebra used for mixed-symmetry HS fields in flat spaces [Buchbinder, I.L.; et al. Nucl. Phys. B 2012, 862, 270–326]. Polynomial deformations of the su(1,1) algebra related to the Bethe ansatz are studied as a byproduct. A nilpotent BRST operator for a non-linear HS symmetry algebra of the converted constraints for Y(s1,s2) is found, with non-vanishing terms (resolving the Jacobi identities) of the third order in powers of ghost coordinates. A gauge-invariant unconstrained reducible Lagrangian formulation for a free bosonic HS field of generalized spin (s1,s2) is deduced. Following the results of [Buchbinder, I.L.; et al. Phys. Lett. B 2021, 820, 136470.; Buchbinder, I.L.; et al. arXiv 2022, arXiv:2212.07097], we develop a BRST approach to constructing general off-shell local cubic interaction vertices for irreducible massive higher-spin fields (being candidates for massive particles in the Dark Matter problem). A new reducible gauge-invariant Lagrangian formulation for an antisymmetric massive tensor field of spin (1,1) is obtained.

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BRST-BV quantum actions for constrained totally-symmetric integer HS fields

Cited by 8 publications

References 59 publications

Towards the structure of a cubic interaction vertex for massless integer higher spin fields

Towards the structure of a cubic interaction vertex for massless integer higher spin fields

Covariant Cubic Interacting Vertices for Massless and Massive Integer Higher Spin Fields

Gauge-Invariant Lagrangian Formulations for Mixed-Symmetry Higher-Spin Bosonic Fields in AdS Spaces

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