Conformal Higher Spin Symmetries of 4d Massless Supermultiplets and $osp(L,2M)$ Invariant Equations in Generalized (Super)Space

Abstract

Realization of the conformal higher spin symmetry on the 4d massless field supermultiplets is given. The self-conjugated supermultiplets, including the linearized $\mathcal{N}=4$ SYM theory, are considered in some detail. Duality between non-unitary field-theoretical representations and the unitary doubleton--type representations of the 4d conformal algebra $su(2,2)$ is formulated in terms of a Bogolyubov transform. The set of 4d massless fields of all spins is shown to form a representation of $sp(8)$. The obtained results are extended to the generalized superspace invariant under $osp(L,2M)$ supersymmetries. World line particle interpretation of the free higher spin theories in the $osp(2\mathbb{N},2M)$ invariant (super)space is given. Compatible with unitarity free equations of motion in the $osp(L,2M)$ invariant (super)space are formulated. A conjecture on the chain of $Ad{S}_{d+1}/CF{T}_d\to Ad{S}_d/CF{T}_{d-1}\to ...$ dualities in the higher spin gauge theories is proposed.

Latex, 63 pages; no figures.V2 Typos corrected, References updated. V3.Typos correced, references and an explanation on the relationship with previous work in section 4 are added. The version to appear in Phys.Rev.D

References in corpus (13)

• Stringy gravity, interacting tensionless strings and massless higher spins
• Cubic Interactions of Bosonic Higher Spin Gauge Fields in $Ad{S}_5$
• Doubletons and 5D Higher Spin Gauge Theory
• On the mixed symmetry irreducible representations of the Poincare group in the BRST approach
• Towards Massless Higher Spin Extension of D=5, N=8 Gauged Supergravity
• Progress in Higher Spin Gauge Theories
• Massless arbitrary spin fields in AdS(5)
• Hidden Symmetries, Central Charges and All That
• Radial Dimensional Reduction: (Anti) de Sitter Theories from Flat
• Free fermionic higher spin fields in AdS(5)
• Strings in a Space with Tensor Central Charge Coordinates
• Uniform Twistor-Like Formulation of Massive and Massless Superparticles with Tensorial Central Charges
• Symplectic vs pseudo-Euclidean space-time with extra dimensions

Cited by in corpus (109)

• AdS Dual of the Critical O(N) Vector Model
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Massless Higher Spins and Holography
• Higher Spin Gauge Theory and Holography: The Three-Point Functions
• How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples
• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• The Higher Spin/Vector Model Duality
• Higher Spin Gauge Theories in Various Dimensions
• Holography of the N=1 Higher-Spin Theory on AdS4
• From Free Fields to $AdS$
• On the uniqueness of higher-spin symmetries in AdS and CFT
• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• Higher Spin Superalgebras in any Dimension and their Representations
• On partition function and Weyl anomaly of conformal higher spin fields
• On the Frame-Like Formulation of Mixed-Symmetry Massless Fields in (A)dS(d)
• From Free Fields to $AdS$ -- III
• Parent field theory and unfolding in BRST first-quantized terms
• Analysis of Higher Spin Field Equations in Four Dimensions
• Bosonic conformal higher--spin fields of any symmetry
• Elements of Vasiliev theory
• Evaluating the AdS dual of the critical O(N) vector model
• Holography, Unfolding and Higher-Spin Theory
• Dynamics of Higher Spin Fields and Tensorial Space
• On Conformal, SL(4,R) and Sp(8,R) Symmetries of 4d Massless Fields
• On N=1,2,4 Higher Spin Gauge Theories in Four Dimensions
• Operator algebra of free conformal currents via twistors
• Higher Spins from Tensorial Charges and OSp(N|2n) Symmetry
• FV-type action for AdS(5) mixed-symmetry fields
• 7D Bosonic Higher Spin Theory: Symmetry Algebra and Linearized Constraints
• Parent form for higher spin fields on anti-de Sitter space
• Higher-Spin Theory and Space-Time Metamorphoses
• Relativity, Causality, Locality, Quantization and Duality in the $Sp(2M)$ Invariant Generalized Space-Time
• On BPS preons, generalized holonomies and D=11 supergravities
• Free Field Dynamics in the Generalized AdS (Super)Space
• Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons
• TASI Lectures on the Higher Spin - CFT duality
• Mixed-symmetry massive fields in AdS(5)
• Partition Functions for Higher-Spin theories in AdS
• The Off-shell (3/2, 2) Supermultiplets Revisited
• Superfield Theories in Tensorial Superspaces and the Dynamics of Higher Spin Fields
• Interactions in Higher-Spin Gravity: a Holographic Perspective
• Multiparticle extension of the higher-spin algebra
• On the Algebraic Structure of Higher-Spin Field Equations and New Exact Solutions
• BPS preons and tensionless super-p-brane in generalized superspace
• Higher Spin Fields in Siegel Space, Currents and Theta Functions
• Off-shell Gauge Fields from BRST Quantization
• Notes on conformal invariance of gauge fields
• Superspace Formulation of 4D Higher Spin Gauge Theory
• Conformal geometry and (super)conformal higher-spin gauge theories
• Towards a gravity dual of the unitary Fermi gas
• Half-integer Higher Spin Fields in (A)dS from Spinning Particle Models
• Mixed-symmetry massless gauge fields in AdS(5)
• On the Holography of Free Yang-Mills
• Supersymmetric string model with 30 kappa--symmetries in an extended D=11 superspace and 30/ 32 BPS states
• Massive twistor particle with spin generated by Souriau-Wess-Zumino term and its quantization
• Extension of the Shirafuji model for Massive Particles with Spin
• $Sp(8)$ invariant higher spin theory, twistors and geometric BRST formulation of unfolded field equations
• Free fermionic higher spin fields in AdS(5)
• Massless higher spin D=4 superparticle with both N=1 supersymmetry and its bosonic counterpart
• Higher Spins in Hyper-Superspace
• Twisted self-duality for higher spin gauge fields and prepotentials
• Higher Spins from Nonlinear Realizations of $OSp(1|8)$
• E_{11} and Higher Spin Theories
• Critical solutions in topologically gauged N=8 CFTs in three dimensions
• Lagrangian conformal higher spin theory
• Scalar Field Corrections to AdS_4 Gravity from Higher Spin Gauge Theory
• Wess-Zumino actions and Dirichlet Boundary Conditions for Super p-branes with Exotic Fractions of Supersymmetry
• Master Higher-Spin Particle
• An infinite supermultiplet of massive higher-spin fields
• A String Model for AdS Gravity and Higher Spins
• Singletons and their maximal symmetry algebras
• Symmetries of higher-spin current interactions in four dimensions
• Vectorial AdS_5/CFT_4 duality for spin-one boundary theory
• Ambitwistors, oscillators and massless fields on $Ad{S}_5$
• A Note on Vectorial AdS${}_5$/CFT${}_4$ Duality for Spin-$j$ Boundary Theory
• On Tensorial Spaces and BCFW Recursion Relations for Higher Spin Fields
• Maxwell group and HS field theory
• Extended supersymmetry in massless conformal higher spin theory
• Geometrical structure of Weyl invariants for spin three gauge field in general gravitational background in $d=4$
• Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields
• New particle model in extended space-time and covariantization of planar Landau dynamics
• On Sp(2M) Invariant Green Functions
• Brane Content of Branes' States
• Aspects of topologically gauged M2-branes with six supersymmetries: towards a "sequential AdS/CFT"?
• Exceptional field theories, superparticles in an enlarged 11D superspace and higher spin theories
• On manifestly sp(2) invariant formulation of quadratic higher spin Lagrangians
• New conformal-like symmetry of strictly massless fermions in four-dimensional de Sitter space
• Extra Gauge Symmetry for Extra Supersymmetry
• Conformal higher-spin symmetries in twistor string theory
• Hamiltonian structure and noncommutativity in $p$-brane models with exotic supersymmetry
• BPS preons and the AdS-M-algebra
• Linearized Coxeter Higher-Spin Theories
• String Amplitudes and Frame-like Formalism for Higher Spins
• Correlation Functions of Sp(2n) Invariant Higher-Spin Systems
• New Model of Higher-Spin Particle
• Canonical formalism and quantization of a massless spinning bosonic particle in four dimensions
• Little Groups of Preon Branes
• Quantum BRST charge and OSp(1|8) superalgebra of twistor-like p-branes with exotic supersymmetry and Weyl symmetry
• Two-twistor particle models and free massive higher spin fields
• Role of the orthogonal group in construction of osp(1|2n) representations
• Conserved Higher-Spin Charges in $Ad{S}_4$
• Scattering amplitudes as multi-particle higher-spin charges in the correspondence space
• Representations of the Lie Superalgebra $\mathfrak{osp}(1|2n)$ with Polynomial Bases
• Worldsheet Free Fields, Higher Spin Symmetry and Free $\mathcal{N}=4$ Super Yang-Mills
• Whether conformal supersymmetry is broken by quantum p-branes with exotic supersymmetry?
• Bosonic Fradkin-Tseytlin equations unfolded. Irreducible case
• Higher-spin fields and charges in the periodic spinor space
• BRST Extension of the Non-Linear Unfolded Formalism
• Symmetry and holonomy in M Theory