Lagrangian conformal higher spin theory

Abstract

In a previous paper conformal gravity was derived by means of a precise action principle on the hypercone in the conformal space. Here it is shown that the same technique used to construct conformal spin two theory as represented by linear conformal gravity may also be used for the construction of conformal higher spin theories. The basic ingredients in these constructions are gauge invariant field strengths (curvatures). In fact, their very existence as manifestly conformal fields requires the present conformal theory. The general form of the actions for the free theories on the hypercone are given. In spacetime these actions are shown to be expressed in terms of squares of generalized Weyl tensors. Conformal spin three and four are calculated explicitly. The theories are proposed to be equivalent to the free theories given by Fradkin and Linetsky. Since the equations are of order 2s a consistent quantization is difficult to achieve but might exist. Interactions are expected to exist and is the motivation behind this approach.

78 pages

References in corpus (15)

• Introduction to the Classical Theory of Higher Spins
• Tensor gauge fields in arbitrary representations of GL(D,R) : duality & Poincare lemma
• Classical and Quantized Tensionless Strings
• Conformal Higher Spin Symmetries of 4d Massless Supermultiplets and $osp(L,2M)$ Invariant Equations in Generalized (Super)Space
• An Introduction to Free Higher-Spin Fields
• Tensor gauge fields in arbitrary representations of GL(D,R): II. Quadratic actions
• Minimal Local Lagrangians for Higher-Spin Geometry
• Dynamics of Higher Spin Fields and Tensorial Space
• On Conformal, SL(4,R) and Sp(8,R) Symmetries of 4d Massless Fields
• Progress in Higher Spin Gauge Theories
• High Spin Gauge Fields and Two-Time Physics
• Infinite spin particles
• Gauge invariants and Killing tensors in higher-spin gauge theories
• Conformal theories including conformal gravity as gauge theories on the hypercone
• Mixed symmetry gauge fields in a flat background

Cited by in corpus (15)

• On partition function and Weyl anomaly of conformal higher spin fields
• Bosonic conformal higher--spin fields of any symmetry
• Partition function of free conformal higher spin theory
• Tractors, Mass and Weyl Invariance
• Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons
• Conformal higher spin scattering amplitudes from twistor space
• A note on higher-derivative actions for free higher-spin fields
• Boundary values of mixed-symmetry massless fields in AdS space
• The Schouten tensor as a connection in the unfolding of 3D conformal higher-spin fields
• Thermal power spectrum in the CFT driven cosmology
• BRST-BV approach to conformal fields
• Lagrangian higher spin field theories from the O(N) extended supersymmetric particle
• Massless chiral fields in six dimensions
• Induced Action for Conformal Higher Spins from Worldline Path Integrals
• Bosonic Fradkin-Tseytlin equations unfolded. Irreducible case