Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields

Abstract

We introduce prepotentials for fermionic higher-spin gauge fields in four spacetime dimensions, generalizing earlier work on bosonic fields. To that end, we first develop tools for handling conformal fermionic higher-spin gauge fields in three dimensions. This is necessary because the prepotentials turn out to be three-dimensional fields that enjoy both "higher-spin diffeomorphism" and "higher-spin Weyl" gauge symmetries. We discuss a number of the key properties of the relevant Cotton tensors. The reformulation of the equations of motion as "twisted self-duality conditions" is then exhibited. We show next how the Hamiltonian constraints can be explicitly solved in terms of appropriate prepotentials and show that the action takes then the same remarkable form for all spins.

arXiv comment25+6 pages, 1 table, v2: 1 reference added

References in corpus (39)

• Conformal Higher Spin Theory
• On the geometry of higher-spin gauge fields
• Conformal Higher Spin Symmetries of 4d Massless Supermultiplets and $osp(L,2M)$ Invariant Equations in Generalized (Super)Space
• On geometric equations and duality for free higher spins
• Duality in linearized gravity
• Massive 3D Supergravity
• Tensor fields of mixed Young symmetry type and N-complexes
• On Higher Derivatives in 3D Gravity and Higher Spin Gauge Theories
• On Conformal, SL(4,R) and Sp(8,R) Symmetries of 4d Massless Fields
• Gauge invariant two-point vertices of shadow fields, AdS/CFT, and conformal fields
• Ordinary-derivative formulation of conformal totally symmetric arbitrary spin bosonic fields
• Off-shell massive N=1 supermultiplets in three dimensions
• Duality invariance of all free bosonic and fermionic gauge fields
• Gravitational duality near de Sitter space
• Extension of the Poincaré group with half-integer spin generators: hypergravity and beyond
• Asymptotically flat structure of hypergravity in three spacetime dimensions
• Higher Spin Conformal Geometry in Three Dimensions and Prepotentials for Higher Spin Gauge Fields
• Higher spin super-Cotton tensors and generalisations of the linear-chiral duality in three dimensions
• A spin-4 analog of 3D massive gravity
• Off-shell higher spin N=2 supermultiplets in three dimensions
• Chiral Tensors of Mixed Young Symmetry
• Gravitational Electric-Magnetic Duality, Gauge Invariance and Twisted Self-Duality
• Topologically massive higher spin gauge theories
• Twisted Self-Duality for Linearized Gravity in D dimensions
• Dual actions for massless, partially-massless and massive gravitons in (A)dS
• The non-linear coupled spin 2 - spin 3 Cotton equation in three dimensions
• Unfolded form of conformal equations in M dimensions and o(M+2)-modules
• Twisted self-duality for higher spin gauge fields and prepotentials
• The Schouten tensor as a connection in the unfolding of 3D conformal higher-spin fields
• On the conformal higher spin unfolded equation for a three-dimensional self-interacting scalar field
• Symmetries of higher-spin current interactions in four dimensions
• Generalized cohomology for irreducible tensor fields of mixed Young symmetry type
• Supersymmetric electric-magnetic duality as a manifest symmetry of the action for super-Maxwell theory and linearized supergravity
• Supersymmetric electric-magnetic duality of hypergravity
• Higher-spin charges in Hamiltonian form. II. Fermi fields
• Duality invariance of $s\ge 3/2$ fermions in AdS
• Spin-2 twisted duality in (A)dS
• Prepotentials for linearized supergravity
• Towards an exact frame formulation of conformal higher spins in three dimensions

Cited by in corpus (9)

• Cubic interactions for arbitrary spin N-extended massless supermultiplets in 4d flat space
• Cubic interaction vertices for N=1 arbitrary spin massless supermultiplets in flat space
• Conformal geometry and (super)conformal higher-spin gauge theories
• Spin projection operators and higher-spin Cotton tensors in three dimensions
• Prepotentials for linearized supergravity
• Higher-spin Cotton tensors and massive gauge-invariant actions in AdS${}_3$
• Superfield approach to interacting N=2 massive and massless supermultiplets in 3d flat space
• On equivalence of gauge-invariant models for massive integer-spin fields
• AdS (super)projectors in three dimensions and partial masslessness