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

Abstract

In this work we present the ultra-relativistic N -extended AdS Chern-Simons supergravity theories in three spacetime dimensions invariant under N -extended AdS Carroll superalgebras. We first consider the (2, 0) and (1, 1) cases; subsequently, we generalize our analysis to N = (N , 0), with N even, and to N = (p, q), with p, q > 0. The N -extended AdS Carroll superalgebras are obtained through the Carrollian (i.e., ultra-relativistic) contraction applied to an so(2) extension of osp(2|2) ⊗ sp(2), to osp(2|1) ⊗ osp(2, 1), to an so(N ) extension of osp(2|N ) ⊗ sp(2), and to the direct sum of an so(p) ⊕ so(q) algebra and osp(2|p) ⊗ osp(2, q), respectively. We also analyze the flat limit (ℓ → ∞, being ℓ the length parameter) of the aforementioned N -extended Chern-Simons AdS Carroll supergravities, in which we recover the ultrarelativistic N -extended (flat) Chern-Simons supergravity theories invariant under N -extended super-Carroll algebras. The flat limit is applied at the level of the superalgebras, Chern-Simons actions, supersymmetry transformation laws, and field equations.The study of spacetime symmetries has proved to be fundamental for analyzing and understanding various physical models. For instance, think of Newtonian gravity, Maxwell's electromagnetism, special and general relativity, string and supergravity theory. Most of these theories are based on relativistic symmetries. On the other hand, during the years models with non-relativistic symmetries have also been developed and analyzed, and and are still the subject of in-depth studies.In this context, Carroll symmetries [1,2], arising when the velocity of light is sent to zero (i.e., in the ultra-relativistic limit, c → 0), have attracted some interest over recent years. 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. 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. Afterwards, in [15], the AdS Carroll CS gravity theory was discussed for the first time. 1 Non-relativistic symmetry groups play a remarkable role also in holography [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. More specifically, in the work [24], connections among Carrollian physics, holography of flat space, and the Bondi-Metzner-Sachs (BMS) algebra were discove...

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

“…Note added. While this manuscript was being finalised, the preprints [38,39] appeared on the arXiv that have some overlap with some of our results.…”

“…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…”

Three-dimensional non-relativistic extended supergravity with cosmological constant

“…Concerning other possible future developments, it would also be interesting to extend the study to the ultra-relativistic regime, where some results in the context of supergravity have been recently presented in [95,96] [work in progress]. allows us to obtain new expanded Lie (super)algebras which cannot be obtained through other Lie (super)algebra expansion methods.…”

Three-dimensional Maxwellian extended Bargmann supergravity

“…Three-dimensional non-relativistic (NR) and ultra-relativistic (UR) versions of supergravity theory have only been explored recently in [1][2][3][4][5][6][7]. Although several generalizations and applications of supergravity have been developed by diverse authors these last four decades, its NR construction remains challenging and has only been approached in three spacetime dimensions.…”