Point particle in general background fields vs. free gauge theories of traceless symmetric tensors

Point particle may interact to traceless symmetric tensors of arbitrary rank. Free gauge theories of traceless symmetric tensors are constructed, that provides a possibility for a new type of interactions, when particles exchange by those gauge fields. The gauge theories are parameterized by the particle's mass m and otherwise are unique for each rank s. For m=0, they are local gauge models with actions of 2s-th order in derivatives, known in d=4 as "pure spin", or "conformal higher spin" actions by Fradkin and Tseytlin. For nonzero m, each rank-s model undergoes a unique nonlocal deformation which entangles fields of all ranks, starting from s. There exists a nonlocal transform which maps m > 0 theories onto m=0 ones, however, this map degenerates at some m > 0 fields whose polarizations are determined by zeros of Bessel functions. Conformal covariance properties of the m=0 models are analyzed, the space of gauge fields is shown to admit an action of an infinite-dimensional "conformal higher spin" Lie algebra which leaves gauge transformations intact.Comment: 21 pages, remarks on nonlinear generalization added, a mistake in the discussion of degenerate solutions correcte

Conformal Higher Spin Theory

We construct gauge theory of interacting symmetric traceless tensor fields of all ranks s=0,1,2,3, ... which generalizes Weyl-invariant dilaton gravity to the higher spin case, in any dimension d>2. The action is given by the trace of the projector to the subspace with positive eigenvalues of an arbitrary hermitian differential operator H, the symmetric tensor fields emerge after expansion of the latter in power series in derivatives. After decomposition in perturbative series around a conformally flat point H=\Box, the quadratic part of the action breaks up as a sum of free gauge theories of symmetric traceless tensors of rank s with actions of d-4+2s order in derivatives introduced in 4d case by Fradkin and Tseytlin and studied at the cubic order level by Fradkin and Linetsky. Higher orders in interaction are well-defined. We discuss in detail global symmetries of the model which give rise to infinite dimensional conformal higher spin algebras for any d. We stress geometric origin of conformal higher spin fields as background fields of a quantum point particle, and make the conjecture generalizing this geometry to the system "tensionless d-1 brane + Fronsdal higher spin massless fields in d+1 dimensions". We propose a candidate on the role of Higgs-like higher spin compensator able to spontaneously break higher spin symmetries. At last, we make the conjecture that, in even dimensions d, the action of conformal higher spin theory equals the logarithmically divergent term of the action of massless higher spin fields on AdS_{d+1} evaluated on the solutions of Dirichlet-like problem, where conformal higher spin fields are boundary values of massless higher spin fields on AdS_{d+1}, the latter conjecture provides information on the full higher spin action in AdS_{d+1}.Comment: 142 page