paper

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

arXiv:hep-th/0110056 · doi:10.1142/S0217751X03015830

Abstract

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.

21 pages, remarks on nonlinear generalization added, a mistake in the discussion of degenerate solutions corrected

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