Higher spin fields from a worldline perspective

TL;DR

This paper develops a worldline approach to quantize higher spin and conformal fields, providing a compact formula for their physical degrees of freedom across dimensions and gauge groups.

Contribution

It introduces a method to compute the degrees of freedom of higher spin fields using worldline models and orthogonal polynomial techniques, extending previous approaches.

Findings

Derived a universal formula for degrees of freedom in various dimensions.

Computed degrees of freedom for specific SO(4) models with partial gauge fixing.

Provided insights into the structure of higher spin field quantization.

Abstract

Higher spin fields in four dimensions, and more generally conformal fields in arbitrary dimensions, can be described by spinning particle models with a gauged SO(N) extended supergravity on the worldline. We consider here the one-loop quantization of these models by studying the corresponding partition function on the one-dimensional torus. After gauge fixing the supergravity multiplet, the partition function reduces to an integral over the corresponding moduli space which is computed using orthogonal polynomial techniques. We obtain a compact formula which gives the number of physical degrees of freedom for all N in all dimensions. As an aside we compute the physical degrees of freedom of the SO(4) = SU(2)xSU(2) model with only a SU(2) factor gauged, which has attracted some interest in the literature.