Master Actions and Helicity Decomposition for Spin-4 Models in $3D$

TL;DR

This paper develops a master action framework to connect four self-dual models of massive spin-4 particles in 3D, demonstrating their quantum equivalence and utilizing helicity decomposition to ensure consistency.

Contribution

It introduces a novel master action that links multiple spin-4 models and employs helicity decomposition to verify particle content absence.

Findings

Four self-dual models are shown to be quantum equivalent.

Helicity decomposition confirms mixing terms are particle-free.

Geometrical methods aid in describing higher-order models.

Abstract

The present work introduces a master action that interpolates between four self-dual models, $SD(i)$, for describing massive spin-4 particles in $D=2+1$ dimensions. These models are designated by $i=1,2,3$ and $4$, representing the order in derivatives. Our results show that the four descriptions are quantum equivalent through comparison of their correlation functions, up to contact terms. A geometrical approach is demonstrated to be a useful tool in describing the third and fourth order models. The construction of the master action relies on the introduction of mixing terms, which must be free of particle content. We use the helicity decomposition method to verify the absence of particle content in these terms, ensuring the proper functioning of the master action.