<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">N</mml:mi></mml:math>-extended Maxwell supergravities as Chern-Simons theories in three spacetime dimensions

Self Cite

We present a novel three-dimensional non-relativistic Chern-Simons supergravity theory invariant under a Maxwellian extended Bargmann superalgebra. We first study the nonrelativistic limits of the minimal and the N = 2 Maxwell superalgebras. We show that a well-defined Maxwellian extended Bargmann supergravity requires to construct by hand a supersymmetric extension of the Maxwellian extended Bargmann algebra by introducing additional fermionic and bosonic generators. The new non-relativistic supergravity action presented here contains the extended Bargmann supergravity as a sub-case.

Section: Discussionmentioning

confidence: 99%

Section: On the Supersymmetric Extension Of The Maxwellian Extended Bmentioning

confidence: 99%

Section: On the Supersymmetric Extension Of The Maxwellian Extended Bmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Three-dimensional Maxwellian extended Bargmann supergravity

Concha

Ravera

Rodríguez

2020

Self Cite

“…It is well assumed that a (super)gravity theory in three spacetime dimensions can be described by a CS action as a gauge theory, providing a useful toy model to approach higher-dimensional models [43][44][45][46][47][48][49][50][51]. In the last decades, diverse three-dimensional supergravity theories have been studied, and, in this context, there has also been a growing interest to extend AdS and Poincaré supergravity theories to other symmetries (see [39,52] and references therein).…”

Section: Introductionmentioning

confidence: 99%

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

Ali

Ravera

2020

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...

Extended kinematical 3D gravity theories

Concha,

Pino,

Ravera

et al. 2024

In this work, we classify all extended and generalized kinematical Lie algebras that can be obtained by expanding the $$ \mathfrak{so} $$ so (2, 2) algebra. We show that the Lie algebra expansion method based on semigroups reproduces not only the original kinematical algebras but also a family of non- and ultra-relativistic algebras. Remarkably, the extended kinematical algebras obtained as sequential expansions of the AdS algebra are characterized by a non-degenerate bilinear invariant form, ensuring the construction of a well-defined Chern-Simons gravity action in three spacetime dimensions. Contrary to the contraction process, the degeneracy of the non-Lorentzian theories is avoided without extending the relativistic algebra but considering a bigger semigroup. Using the properties of the expansion procedure, we show that our construction also applies at the level of the Chern-Simons action.