Bosonic conformal higher--spin fields of any symmetry

Abstract

Free Lagrangians are found both for gauge and non-gauge bosonic conformal fields of any symmetry type and in any space-time dimension. Conformal gauge fields of various types, their gauge transformations and gauge invariant field strengths (generalized Weyl tensors), which are derived by the ${\sigma }_{-}$ cohomology technics in the frame-like formulation, are shown to correspond to supersymmetric vacua of certain supersymmetric matrix mechanics. The correspondence between conformal and $Ad{S}_d$ higher-spin models, that turn out to have identical generalized Weyl tensors, is discussed.

55 pages, to the memory of Efim Samoilovich Fradkin; v2 minor corrections, comments and references added; V3 typos corrected references updated

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Cited by in corpus (71)

• Cubic Vertices for Symmetric Higher-Spin Gauge Fields in $(A)d{S}_d$
• On the uniqueness of higher-spin symmetries in AdS and CFT
• Higher order singletons, partially massless fields and their boundary values in the ambient approach
• On partition function and Weyl anomaly of conformal higher spin fields
• Classical and quantum stability of higher-derivative dynamics
• Partition function of free conformal higher spin theory
• Gauge fields in (A)dS within the unfolded approach: algebraic aspects
• On matter-free Higher Spin Gravities in 3d: (partially)-massless fields and general structure
• New Conformal Higher Spin Gravities in $3d$
• Massive Higher Spins from BRST and Tractors
• On conformal higher spin wave operators
• Arbitrary spin conformal fields in (A)dS
• Conformal higher spin scattering amplitudes from twistor space
• A note on higher-derivative actions for free higher-spin fields
• Towards higher-spin holography in ambient space of any dimension
• Minimal unitary representation of SU(2,2) and its deformations as massless conformal fields and their supersymmetric extensions
• Duality-invariant (super)conformal higher-spin models
• Notes on the ambient approach to boundary values of AdS gauge fields
• Higher Spin Conformal Geometry in Three Dimensions and Prepotentials for Higher Spin Gauge Fields
• Gravity, Two Times, Tractors, Weyl Invariance and Six Dimensional Quantum Mechanics
• Frame-like Lagrangians and presymplectic AKSZ-type sigma models
• Notes on conformal invariance of gauge fields
• Interacting massive and massless arbitrary spin fields in 4d flat space
• Parent formulation at the Lagrangian level
• Conformal geometry and (super)conformal higher-spin gauge theories
• 6d conformal gravity
• Conformal Higher Spin Theory and Twistor Space Actions
• Anomalous conformal currents, shadow fields and massive AdS fields
• Boundary values of mixed-symmetry massless fields in AdS space
• Iterating free-field AdS/CFT: higher spin partition function relations
• Cubic interactions of arbitrary spin fields in 3d flat space
• Weyl's Gauge Invariance: Conformal Geometry, Spinors, Supersymmetry, and Interactions
• Gauge invariant approach to low-spin anomalous conformal currents and shadow fields
• Mixed-symmetry fields in AdS(5), conformal fields, and AdS/CFT
• The Schouten tensor as a connection in the unfolding of 3D conformal higher-spin fields
• Scattering of conformal higher spin fields
• Massless hook field in AdS(d+1) from the holographic perspective
• New locally (super)conformal gauge models in Bach-flat backgrounds
• Conformal interactions between matter and higher-spin (super)fields
• Metric projective geometry, BGG detour complexes and partially massless gauge theories
• Minkowski superspaces and superstrings as almost real-complex supermanifolds
• Conformal Higher-Spin Gravity: Linearized Spectrum = Symmetry Algebra
• On the structure of the conformal higher-spin wave operators
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• Notes on conformal anomaly, nonlocal effective action and the metamorphosis of the running scale
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• Generalised superconformal higher-spin multiplets
• 3d conformal fields with manifest $sl(2,\mathbb{C})$
• Constructing conformally invariant equations by using Weyl geometry
• Unfolding Conformal Geometry
• Generalised conformal higher-spin fields in curved backgrounds
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• Conformal totally symmetric arbitrary spin fermionic fields
• On higher spin partition functions
• Scale and Conformal Invariance on (A)dS
• Light-cone AdS/CFT-adapted approach to AdS fields/currents, shadows, and conformal fields
• Conformal Lagrangians from the (formal) near boundary analysis of AdS gauge fields
• Self-duality for $\mathcal{N}$-extended superconformal gauge multiplets
• General light-cone gauge approach to conformal fields and applications to scalar and vector fields
• Massless chiral fields in six dimensions
• Induced Action for Conformal Higher Spins from Worldline Path Integrals
• Jung-type Inequalities and Blaschke-Santaló Diagrams for Different Diameter Variants
• Group manifold approach to higher spin theory
• Higher-Rank Fields and Currents
• Bosonic Fradkin-Tseytlin equations unfolded. Irreducible case
• Scale- versus Conformal Invariance Revisited