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

Abstract

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 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.

Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity

“…where we have used the field redefinition (4.17). This corresponds to Carrollian AdS Chern-Simons gravity [39,56] and reduces to three-dimensional Carroll gravity [57,58,43] in the vanishing cosmological constant limit. 6 Using also (4.20), the second term of the sum reads…”

Nonrelativistic limits of colored gravity in three dimensions

“…These nonrelativistic gravity theories are sometimes called extended Bargmann gravity and extended NH gravity, respectively. Along the same lines, the nonrelativistic Chern-Simons theories admit various extensions according to the symmetry algebras [17][18][19].…”

$$ \mathcal{N} $$-extended Chern-Simons Carrollian supergravities in 2 + 1 spacetime dimensions

“…In fact, models with Carroll symmetries occurred in the literature in the study of tachyon condensation [3], warped conformal field theories [4], and tensionless strings [5][6][7][8][9]. Moreover, a study exploring the Carroll limit corresponding to M2-as well as M3-branes propagating over D = 11 supergravity backgrounds in M-theory has been recently presented in [10].Concerning gravity theories, models of Carrollian (i.e., ultra-relativistic) gravity have been developed and analyzed in [11][12][13]. In particular, non-and ultra-relativistic Chern-Simons (CS) type actions in 2 + 1 dimensions were constructed in [12], where the authors included a spin-3 field coupled to gravity.…”

“…Moreover, a study exploring the Carroll limit corresponding to M2-as well as M3-branes propagating over D = 11 supergravity backgrounds in M-theory has been recently presented in [10].Concerning gravity theories, models of Carrollian (i.e., ultra-relativistic) gravity have been developed and analyzed in [11][12][13]. In particular, non-and ultra-relativistic Chern-Simons (CS) type actions in 2 + 1 dimensions were constructed in [12], where the authors included a spin-3 field coupled to gravity. The geometry of flat and Anti-de Sitter (AdS) Carroll spaces were investigated, both in the bosonic as well as in the supersymmetric case, in [14], were the authors focused on the symmetries of a particle moving in such spaces.…”

“…Concerning gravity theories, models of Carrollian (i.e., ultra-relativistic) gravity have been developed and analyzed in [11][12][13]. In particular, non-and ultra-relativistic Chern-Simons (CS) type actions in 2 + 1 dimensions were constructed in [12], where the authors included a spin-3 field coupled to gravity.…”