Dual descriptions of massive spin-3 particles in $D=2+1$ via Noether gauge embedment

TL;DR

This paper explores the relationships among various massive spin-3 particle models in 2+1 dimensions using the Noether Gauge Embedment method, systematically deriving higher-order self-dual models with auxiliary fields to eliminate ghosts.

Contribution

It introduces a systematic approach to derive a sequence of self-dual models for spin-3 particles via NGE, including auxiliary fields for ghost elimination.

Findings

Derived a sequence of four self-dual models for spin-3 particles.

Automated generation of auxiliary fields for ghost removal.

Established the correct form of the 4th order self-dual model.

Abstract

We present here a relationship among massive self-dual models for spin-3 particles in $D=2+1$ via the Noether Gauge Embedment $(NGE)$ procedure. Starting with a first order model (in derivatives) $S_{SD(1)}$ we have obtained a sequence of four self-dual models $S_{SD(i)}$ where $i=1,2,3,4$. We demonstrate that the $NGE$ procedure generate the correct action for the auxiliary fields automatically. We obtain the whole action for the $4th$ order self-dual model including all the needed auxiliary fields to get rid of the ghosts of the theory.