Notes on conformal invariance of gauge fields

Abstract

In Lagrangian gauge systems, the vector space of global reducibility parameters forms a module under the Lie algebra of symmetries of the action. Since the classification of global reducibility parameters is generically easier than the classification of symmetries of the action, this fact can be used to constrain the latter when knowing the former. We apply this strategy and its generalization for the non-Lagrangian setting to the problem of conformal symmetry of various free higher spin gauge fields. This scheme allows one to show that, in terms of potentials, massless higher spin gauge fields in Minkowski space and partially-massless fields in (A)dS space are not conformal for spin strictly greater than one, while in terms of curvatures, maximal-depth partially-massless fields in four dimensions are also not conformal, unlike the closely related, but less constrained, maximal-depth Fradkin--Tseytlin fields.

38 pages

References in corpus (12)

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Cited by in corpus (21)

• Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal
• On matter-free Higher Spin Gravities in 3d: (partially)-massless fields and general structure
• New Conformal Higher Spin Gravities in $3d$
• Continuous spin fields of mixed-symmetry type
• From Higher Spins to Strings: A Primer
• Unified formulation for helicity and continuous spin fermionic fields
• Gauge PDE and AKSZ-type Sigma Models
• Boundary values of mixed-symmetry massless fields in AdS space
• Partially Massless Monopoles and Charges
• Iterating free-field AdS/CFT: higher spin partition function relations
• The Schouten tensor as a connection in the unfolding of 3D conformal higher-spin fields
• Scale vs. Conformal Invariance at the IR Fixed Point of Quantum Gravity
• A Note on Vectorial AdS${}_5$/CFT${}_4$ Duality for Spin-$j$ Boundary Theory
• Conformally covariant operators of mixed-symmetry tensors and MAGs
• Generalised superconformal higher-spin multiplets
• New conformal-like symmetry of strictly massless fermions in four-dimensional de Sitter space
• Scale and Conformal Invariance on (A)dS
• On correlation functions of higher-spin currents in arbitrary dimensions $d>3$
• Hidden Conformal Symmetry of the Discrete Series Scalars in dS${}_2$
• Unconventional conformal invariance of maximal depth partially massless fields on $d{S}_4$ and its relation to complex partially massless SUSY
• Massless chiral fields in six dimensions