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

Abstract

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 $Y(s_1,\dots ,s_k)$ with $k\ge 2$ 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 \cite{BRbos}. Polynomial deformations of the $su(1,1)$ algebra related to the Bethe ansatz are studied as a by-product. A nilpotent BRST operator for a non-linear HS symmetry algebra of the converted constraints for $Y(s_1,s_2)$ is found, with non-vanishing terms (resolving the Jacobi identities) of third order in powers of ghost coordinates. A gauge-invariant unconstrained reducible Lagrangian formulation for a free bosonic HS field of generalized spin $(s_1,s_2)$ is deduced. Following the results of \cite{BuchbinderReshetnyak, BRmasscub}, 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.

71 pages, 1 figure, presentation clarified and improved, relation to Cosmology and 11 references added; elaborated and developed conference paper [arXiv:1111.5516[hep-th]], published version in Universe

References in corpus (40)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• A Theory of Dark Matter
• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space
• A generating function for the cubic interactions of higher spin fields
• BRST approach to Lagrangian construction for fermionic higher spin fields in AdS space
• Frame-like gauge invariant formulation for massive high spin particles
• BRST-BV approach to cubic interaction vertices for massive and massless higher-spin fields
• Constructing the Cubic Interaction Vertex of Higher Spin Gauge Fields
• Unconstrained Higher Spins of Mixed Symmetry. I. Bose Fields
• Finite-time Cosmological Singularities and the Possible Fate of the Universe
• Lepton Jets from Radiating Dark Matter
• Origin of Sterile Neutrino Dark Matter via Vector Secret Neutrino Interactions
• Gauge invariant Lagrangian construction for massive bosonic mixed symmetry higher spin fields
• Higher-Spin Theory and Space-Time Metamorphoses
• Toward frame-like gauge invariant formulation for massive mixed symmetry bosonic fields
• Self-gravitating Vector Dark Matter
• On Lagrangian formulation of Higher Spin Theories on AdS
• Basic introduction to higher-spin theories
• On holomorphic sector of higher-spin theory
• Cubic Vertices for N=1 Supersymmetric Massless Higher Spin Fields in Various Dimensions
• Interacting massive and massless arbitrary spin fields in 4d flat space
• General Cubic Interacting Vertex for Massless Integer Higher Spin Fields
• Cubic interaction vertices for massless higher spin supermultiplets in d=4
• Projectively-Compact Spinor Vertices and Space-Time Spin-Locality in Higher-Spin Theory
• Joint reconstructions of growth and expansion histories from stage-IV surveys with minimal assumptions. II. Modified gravity and massive neutrinos
• BRST approach to Lagrangian formulation of bosonic totally antisymmeric tensor fields in curved space
• Planar solutions of higher-spin theory. Nonlinear corrections
• Mixed-symmetry continuous-spin fields in flat and AdS spaces
• Classical BRST charge for nonlinear algebras
• Mixed-symmetry fields in AdS(5), conformal fields, and AdS/CFT
• Higher Spin Gravities and Presymplectic AKSZ Models
• Light-cone gauge massive and partially-massless fields in AdS(4)
• BRST-BV Quantum Actions for Constrained Totally-Symmetric Integer HS Fields
• Cubic interactions of d4 irreducible massless higher spin fields within BRST approach
• BRST-BV approach for interacting higher spin fields
• Towards the structure of a cubic interaction vertex for massless integer higher spin fields
• Consistent Lagrangians for irreducible interacting higher-spin fields with holonomic constraints
• Non-Abelian gauge theories with composite fields in the background field method

Cited by in corpus (2)

• Covariant Cubic Interacting Vertices for Massless and Massive Integer Higher Spin Fields
• Diagonalization Procedure for Reducible Massless N=1 Supermultiplets