Consistent Lagrangians for irreducible interacting higher-spin fields with holonomic constraints

Abstract

We study the aspects of constructing the interactions for the higher spin fields in the framework of BRST approach. The main object of such an approach is BRST operator acting in the appropriate Fock space and building on the base of constraints that define the irreducible higher spin representations. In its turn, the constrains are divided into differential and purely algebraic or holonomic. The necessary and sufficient conditions to derive the consistent Lagrangian formulations for irreducible interacting higher-spin fields within approach with incomplete BRST operator, where the algebraic constraints are not included into definition of the BRST operator but imposed "by hands" on the field and gauge parameter vectors, are considered. It is shown that in addition to that such constraints should (anti)commute with the BRST operator and annihilate the fields and gauge parameters Fock space vectors, they must form the Abelian (super)algebra both with the BRST operator above and with operators of cubic, quartic and etc. vertices. Only under the above conditions, the formulations with complete and incomplete BRST charges turn out to be equivalent and yield to the same interaction vertices in terms of irreducible fields.

arXiv comment11 pages, minor changes, presentation improved, Contribution to Proceedings of International Workshop "Supersymmetries and Quantum Symmetries 2022"

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Cited by in corpus (4)

• Bilinear Fronsdal currents in the $Ad{S}_4$ higher-spin theory
• Gauge Invariant Lagrangian Formulations for Mixed Symmetry Higher Spin Bosonic Fields in AdS Spaces
• Covariant Lagrangian Cubic Interaction Vertices For Irreducible Higher Spin Fields in Minkowski Backgrounds
• Towards Lagrangian dynamics for constrained mixed-symmetric interacting higher-spin fields