On massive higher spins in d=3

TL;DR

This paper develops a gauge-invariant framework for massive higher spin fields in three dimensions, proving it describes a single physical degree of freedom and connecting it to known self-dual models.

Contribution

It provides the first proof that a gauge-invariant description in d=3 captures exactly one massive degree of freedom, linking it to existing self-dual formulations.

Findings

Confirmed the gauge-invariant formulation describes one physical degree of freedom.

Showed auxiliary fields vanish on-shell after gauge fixing.

Connected the formulation to known self-dual massive spin models.

Abstract

In this paper we consider a frame-like gauge invariant description of massive higher spin bosons and fermions in d=3 and provide for the first time a proof that such formulation does describe just one massive physical degree of freedom with the appropriate helicity. For this purpose we completely fix all the gauge symmetries and show that all other auxiliary components vanish on-shell, while the only remaining highest component satisfies the correct equations. As a bonus, we show that the Lagrangians for the so-called self-dual massive spin-3 and spin-4 fields proposed by Aragone and Khoudeir (as well as their generalization to arbitrary integer and half-integer spins) can be obtained from the gauge invariant ones by the appropriate gauge fixing.