Higher order self-dual models for spin-3 particles in $D=2+1$

Abstract

In $D=2+1$ dimensions, elementary particles of a given helicity can be described by local Lagrangians (parity singlets). By means of a "soldering" procedure two opposite helicities can be joined together and give rise to massive spin-$s$ particles carrying both helicities $\pm s$ (parity doublets), such Lagrangians can also be used in $D=3+1$ to describe massive spin-$s$ particles. From this point of view the parity singlets (self-dual models) in $D=2+1$ are the building blocks of real massive elementary particles in $D=3+1$. In the three cases $s=1,3/2,2$ there are $2s$ self-dual models of order $1,2,\cdots ,2s$ in derivatives. In the spin-3 case the 5th order model is missing in the literature. Here we deduce a 5th order spin-3 self-dual model and fill up this gap. It is shown to be ghost free by means of a master action which relates it with the top model of 6th order. We believe that our approach can be generalized to arbitrary integer spin-$s$ in order to obtain the models of order $2s$ and $2s-1$. We also comment on the difficulties in relating the 5th order model with their lower order duals.

References in corpus (10)

• Massive Gravity in Three Dimensions
• Ghost-free, finite, fourth order D=3 (alas) gravity
• Fundamental theorem on gauge fixing at the action level
• Ghost-free theories with arbitrary higher-order time derivatives
• A new spin-2 self-dual model in $D=2+1$
• Dual descriptions of spin two massive particles in $D=2+1$ via master actions
• Generalized soldering of $\pm 2$ helicity states in $D=2+1$
• Dual descriptions of massive spin-3 particles in $D=2+1$ via Noether gauge embedment
• Duality of parity doublets of helicity $\pm 2$ in $D=2+1$
• Soldering spin-3/2 fermions in $D=2+1$

Cited by in corpus (5)

• On higher spin analogues of linearized Topologically Massive Gravity and linearized "New Massive Gravity"
• Soldering spin-3 opposite helicities in $D=2+1$
• Unitarity of Singh-Hagen model in $D$ dimensions
• Self-dual models in $D=2+1$ from dimensional reduction
• Parity singlets and doublets of massive spin-3 particles in $D=2+1$ via Nother gauge embedding