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

TL;DR

This paper explores gauge theories of traceless symmetric tensors interacting with point particles, revealing new nonlocal deformations and conformal properties, with implications for higher spin theories and particle interactions.

Contribution

It constructs free gauge theories for traceless symmetric tensors of arbitrary rank, introduces nonlocal deformations for nonzero mass, and analyzes their conformal symmetry properties.

Findings

Gauge theories parameterized by particle mass and tensor rank.

Existence of nonlocal deformations connecting massive and massless models.

Conformal higher spin algebra acts on the space of gauge fields.

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.