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

Eric Bergshoeff*, Daniel Grumiller, Stefan Prohazka, Jan Rosseel

*Corresponding author for this work

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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 Inonti-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.

Original languageEnglish
Article number114
Number of pages49
JournalJournal of High Energy Physics
Issue number1
Publication statusPublished - 25-Jan-2017


  • Higher Spin Gravity
  • Higher Spin Symmetry
  • Chern-Simons Theories
  • Space-Time Symmetries

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