Master actions for massive spin-3 particles in D=2+1

TL;DR

This paper explores the relationships among various self-dual models for massive spin-3 particles in 2+1 dimensions using the master action approach, highlighting the limitations in increasing derivative order and comparing with spin-2 models.

Contribution

It constructs a master action linking four self-dual models for spin-3 particles and analyzes the impossibility of extending to higher-order models, providing new insights into their structure.

Findings

Constructed a master action interpolating four self-dual models.

Identified reasons preventing higher-order models beyond the fourth order.

Compared spin-3 fourth order term with the spin-2 case.

Abstract

We present here a relationship among massive self-dual models for spin-3 particles in $D=2+1$ via the master action procedure. Starting with a first order model (in derivatives) $S_{SD(1)}$ we have constructed a master action which interpolates among a sequence of four self-dual models $S_{SD(i)}$ where $i=1,2,3,4$. By analyzing the particle content of mixing terms, we give additional arguments that explain why it is apparently impossible to jump from the fourth order model to a higher order model. We have also analyzed similarities and differences between the fourth order $K$-term in the spin-2 case and the analogous fourth order term in the spin-3 context.