Three-dimensional Spin-3 Theories Based on General Kinematical Algebras

TL;DR

This paper explores non- and ultra-relativistic spin-3 theories in three dimensions, classifies related kinematical algebras, and constructs associated Chern--Simons actions, extending to infinite-dimensional symmetries in Carroll Gravity.

Contribution

It systematically classifies all kinematical algebras for spin-3 theories via Inönü–Wigner contractions and constructs their actions, including infinite-dimensional extensions in Carroll Gravity.

Findings

Classified all possible kinematical algebras for spin-3 in 3D.

Constructed Chern--Simons actions for these algebras.

Extended to infinite-dimensional asymptotic symmetry algebras.

Abstract

We initiate the study of non- and ultra-relativistic higher spin theories. For sake of simplicity we focus on the spin-3 case in three dimensions. We classify all kinematical algebras that can be obtained by all possible In\"on\"u--Wigner contraction procedures of the kinematical algebra of spin-3 theory in three dimensional (anti-) de Sitter space-time. We demonstrate how to construct associated actions of Chern--Simons type, directly in the ultra-relativistic case and by suitable algebraic extensions in the non-relativistic case. We show how to give these kinematical algebras an infinite-dimensional lift by imposing suitable boundary conditions in a theory we call "Carroll Gravity", whose asymptotic symmetry algebra turns out to be an infinite-dimensional extension of the Carroll algebra.