On the supersymmetry invariance of flat supergravity with boundary

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In this work we study a non-relativistic three dimensional Chern-Simons gravity theory based on an enlargement of the Extended Bargmann algebra. A finite non-relativistic Chern-Simons gravity action is obtained through the non-relativistic contraction of a particular U (1) enlargement of the so-called AdS-Lorentz algebra. We show that the non-relativistic gravity theory introduced here reproduces the Maxwellian Exotic Bargmann gravity theory when a flat limit ℓ → ∞ is applied. We also present an alternative procedure to obtain the non-relativistic versions of the AdS-Lorentz and Maxwell algebras through the semigroup expansion method.

Section: Maxwellian Exotic Bargmann Algebramentioning

confidence: 99%

Non-relativistic gravity theory based on an enlargement of the extended Bargmann algebra

Concha

Rodríguez

2019

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“…At the supersymmetric level, the minimal Maxwell superalgebra appears to describe a constant Abelian supersymmetric gauge field background in a four-dimensional superspace [56]. Generalizations of the Maxwell superalgebras have then been explored with diverse applications [57][58][59][60][61][62][63][64][65][66]. More recently, a three-dimensional CS supergravity theory invariant under the Maxwell superalgebra and its N -extended versions have been explored in [67][68][69][70].…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional Maxwellian extended Bargmann supergravity

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Ravera

Rodríguez

2020

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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.

“…The recently discovered relations among the Carrollian world and flat holography suggest that this work might represents a starting point to go further in the analysis of supersymmetry invariance of flat supergravity in the presence of a non-trivial boundary, along the lines of [55]. Besides, now, having well-defined three-dimensional CS (super)gravity theories respectively invariant under the N -extended AdS-Carroll and Carroll (super)algebras, it would be intriguing to go beyond and study the asymptotic symmetry of these models, following, for instance, the prescription given in Ref.…”

Section: Discussionmentioning

confidence: 93%

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

Ali

Ravera

2020

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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...