Journal of High Energy Physics

, 2017:114 | Cite as

Three-dimensional spin-3 theories based on general kinematical algebras

  • Eric Bergshoeff
  • Daniel Grumiller
  • Stefan Prohazka
  • Jan Rosseel
Open Access
Regular Article - Theoretical Physics


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 Inönü-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.


Higher Spin Gravity Higher Spin Symmetry Chern-Simons Theories SpaceTime Symmetries 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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© The Author(s) 2017

Authors and Affiliations

  1. 1.Van Swinderen Institute for Particle Physics and GravityUniversity of GroningenGroningenThe Netherlands
  2. 2.Institute for Theoretical PhysicsTU WienViennaAustria
  3. 3.Albert Einstein Center for Fundamental PhysicsUniversity of BernBernSwitzerland
  4. 4.Faculty of PhysicsUniversity of ViennaViennaAustria

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