Higher Spin Conformal Geometry in Three Dimensions and Prepotentials for Higher Spin Gauge Fields

Abstract

We study systematically the conformal geometry of higher spin bosonic gauge fields in three spacetime dimensions. We recall the definition of the Cotton tensor for higher spins and establish a number of its properties that turn out to be key in solving in terms of prepotentials the constraint equations of the Hamiltonian (3 + 1) formulation of four-dimensional higher spin gauge fields. The prepotentials are shown to exhibit higher spin conformal symmetry. Just as for spins 1 and 2, they provide a remarkably simple, manifestly duality invariant formulation of the theory. While the higher spin conformal geometry is developed for arbitrary bosonic spin, we explicitly perform the Hamiltonian analysis and derive the solution of the constraints only in the illustrative case of spin 3. In a separate publication, the Hamiltonian analysis in terms of prepotentials is extended to all bosonic higher spins using the conformal tools of this paper, and the same emergence of higher spin conformal symmetry is confirmed.

32 pages, typos in formulas (3.3), (3.5), (7.3) and (7.4) corrected

References in corpus (4)

• Partition function of free conformal higher spin theory
• On Conformal, SL(4,R) and Sp(8,R) Symmetries of 4d Massless Fields
• On conformal higher spin wave operators
• Higher Spins in Hyperspace

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• Off-shell higher spin N=2 supermultiplets in three dimensions
• Chiral Tensors of Mixed Young Symmetry
• Looking for partially-massless gravity
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• Higher spin de Sitter quasinormal modes
• The non-linear coupled spin 2 - spin 3 Cotton equation in three dimensions
• Twisted self-duality for higher spin gauge fields and prepotentials
• Cubic interactions of arbitrary spin fields in 3d flat space
• The Schouten tensor as a connection in the unfolding of 3D conformal higher-spin fields
• One-loop effective actions and higher spins. II
• A note on the double dual graviton
• The Action of the (free) $(4,0)$-theory
• Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields
• On higher spin analogues of linearized Topologically Massive Gravity and linearized "New Massive Gravity"
• Higher-spin charges in Hamiltonian form. I. Bose fields
• Long, partial-short, and special conformal fields
• Higher-spin Cotton tensors and massive gauge-invariant actions in AdS${}_3$
• Prepotentials for linearized supergravity
• Soldering spin-3 opposite helicities in $D=2+1$
• On equivalence of gauge-invariant models for massive integer-spin fields
• Enhanced Conformal $BM{S}_3$ Symmetries
• Reaching out a "geometrical" description for spin-4 self-dual models in $D=2+1$
• AdS (super)projectors in three dimensions and partial masslessness