Research Outputs
Three-dimensional non-relativistic supergravity and torsion
In this paper we present a torsional non-relativi-stic Chern–Simons (super)gravity theory in three spacetime dimensions. We start by developing the non-relativistic limit of the purely bosonic relativistic teleparallel Chern–Simons formulation of gravity. On-shell the latter yields a non-Riemannian setup with non-vanishing torsion, which, at non-relativistic level, translates into a non-vanishing spatial torsion sourced by the cosmological constant. Then we consider the three-dimensional relativistic N= 2 teleparallel Chern–Simons supergravity theory and obtain its non-relativistic counterpart by exploiting a Lie algebra expansion method. The non-relativistic supergravity theory is characterized, on-shell, by a non-vanishing spatial super-torsion, again sourced by the cosmological constant.
Non-relativistic limit of the Mielke–Baekler gravity theory
In this paper, we present a generalized nonrelativistic Chern–Simons gravity model in three spacetime dimensions. We first study the non-relativistic limit of the Mielke–Baekler gravity through a contraction process. The resulting non-relativistic theory contains a source for the spatial component of the torsion and the curvature measured in terms of two parameters, denoted by p and q. We then extend our results by defining a Newtonian version of the Mielke–Baekler gravity theory, based on a Newtonian like algebra which is obtained from the non-relativistic limit of an enhanced and enlarged relativistic algebra. Remarkably, in both cases, different known non-relativistic and Newtonian gravity theories can be derived by fixing the (p, q) parameters. In particular, torsionless models are recovered for q = 0.
Asymptotic symmetries of three-dimensional Chern-Simons gravity for the Maxwell algebra
We study a three-dimensional Chern-Simons gravity theory based on the Maxwell algebra. We find that the boundary dynamics is described by an enlargement and deformation of the bms3 algebra with three independent central charges. This symmetry arises from a gravity action invariant under the local Maxwell group and is characterized by presence of Abelian generators which modify the commutation relations of the supertranslations in the standard bms3 algebra. Our analysis is based on the charge algebra of the theory in the BMS gauge, which includes the known solutions of standard asymptotically flat case. The field content of the theory is different than the one of General Relativity, but it includes all its geometries as particular solutions. In this line, we also study the stationary solutions of the theory in ADM form and we show that the vacuum energy and the vacuum angular momentum of the stationary configuration are influenced by the presence of the gravitational Maxwell field.
Enlarged super-𝔟𝔪𝔰3 algebra and its flat limit
In this paper we analyze the asymptotic symmetries of the three-dimensional Chern-Simons supergravity for a supersymmetric extension of the semisimple enlargement of the Poincaré algebra, also known as AdSLorentz superalgebra, which is characterized by two fermionic generators. We propose a consistent set of asymptotic boundary conditions for the aforementioned supergravity theory, and we show that the corresponding charge algebra defines a supersymmetric extension of the semisimple enlargement of the bms3 algebra, with three independent central charges. This asymptotic symmetry algebra can alternatively be written as the direct sum of three copies of the Virasoro algebra, two of which are augmented by supersymmetry. Interestingly, we show that the flat limit of the obtained asymptotic algebra corresponds to a deformed super-bms3 algebra, being the charge algebra of the minimal Maxwell supergravity theory in three dimensions.
Asymptotic symmetries of Maxwell Chern–Simons gravity with torsion
We present a three-dimensional Chern–Simons gravity based on a deformation of the Maxwell algebra. This symmetry allows introduction of a non-vanishing torsion to the Maxwell Chern–Simons theory, whose action recovers the Mielke–Baekler model for particular values of the coupling constants. By considering suitable boundary conditions, we show that the asymptotic symmetry is given by the bms3 ⊕ vir algebra with three independent central charges.
Non-relativistic and ultra-relativistic expansions of three-dimensional spin-3 gravity theories
In this paper, we present novel and known non-relativistic and ultra-relativistic spin-3 algebras, by considering the Lie algebra expansion method. We start by applying the expansion procedure using different semigroups to the spin-3 extension of the AdS algebra, leading to spin-3 extensions of known non-relativistic and ultra-relativistic algebras. We then generalize the procedure considering an infinite-dimensional semigroup, which allows to obtain a spin-3 extension of two new infinite families of the Newton-Hooke type and AdS Carroll type. We also present the construction of the gravity theories based on the aforementioned algebras. In particular, the expansion method based on semigroups also allows to derive the (non-degenerate) invariant bilinear forms, ensuring the proper construction of the Chern-Simons gravity actions. Interestingly, in the vanishing cosmological constant limit we recover the spin-3 extensions of the infinite-dimensional Galilean and infinite-dimensional Carroll gravity theories.
Three-dimensional teleparallel Chern-Simons supergravity theory
In this work we present a gauge-invariant threedimensional teleparallel supergravity theory using the ChernSimons formalism. The present construction is based on a supersymmetric extension of a particular deformation of the Poincaré algebra. At the bosonic level the theory describes a non-Riemannian geometry with a non-vanishing torsion. In presence of supersymmetry, the teleparallel supergravity theory is characterized by a non-vanishing super-torsion in which the cosmological constant can be seen as a source for the torsion. We show that the teleparallel supergravity theory presented here reproduces the Poincaré supergravity in the vanishing cosmological limit. The extension of our results to N = p + q supersymmetries is also explored.
Resonant superalgebras and N=1 supergravity theories in three spacetime dimensions
We explore N=1supersymmetric extensions of algebras going beyond the Poincaré and AdS ones in three spacetime dimensions. Besides reproducing two known examples, we present new superalgebras, which all correspond to supersymmetric extensions with one fermionic charge Qαconcerning the so-called resonant algebras being characterized by the presence of an additional bosonic generator Za. We point out particular requirements that superalgebras have to satisfy to be successfully incorporated within valid supergravity actions. The presented algebraic and Lagrangian framework helps us better understand the relations between the various supergravity and supersymmetric Chern-Simons actions invariant under diverse resonant
Observations on BI from N = 2 supergravity and the general Ward identity
The multi-vector generalization of a rigid, partially-broken N = 2 supersymmetric theory is presented as a rigid limit of a suitable gauged N = 2 supergravity with electric, magnetic charges and antisymmetric tensor fields. This on the one hand generalizes a known result by Ferrara, Girardello and Porrati while on the other hand allows to recover the multi-vector BI models of [4] from N = 2 supergravity as the end-point of a hierarchical limit in which the Planck mass first and then the supersymmetry breaking scale are sent to infinity. We define, in the parent supergravity model, a new symplectic frame in which, in the rigid limit, manifest symplectic invariance is preserved and the electric and magnetic Fayet-Iliopoulos terms are fully originated from the dyonic components of the embedding tensor. The supergravity origin of several features of the resulting rigid supersymmetric theory are then elucidated, such as the presence of a traceless SU(2)- Lie algebra term in the Ward identity and the existence of a central charge in the supersymmetry algebra which manifests itself as a harmless gauge transformation on the gauge vectors of the rigid theory; we show that this effect can be interpreted as a kind of “superspace non-locality” which does not affect the rigid theory on space-time. To set the stage of our analysis we take the opportunity in this paper to provide and prove the relevant identities of the most general dyonic gauging of Special-Kaehler and Quaternionic-Kaehler isometries in a generic N = 2 model, which include the supersymmetry Ward identity, in a fully symplectic-covariant formalism.
Non-relativistic gravity theories in four spacetime dimensions
In this work we present a non-relativistic gravity theory defined in four spacetime dimensions using the MacDowell-Mansouri geometrical formulation. We obtain a Newtonian gravity action which is constructed from the curvature of a Newton-Hooke version of the so-called Newtonian algebra. We show that the non-relativistic gravity theory presented here contains the Poisson equation in presence of a cosmological constant. Moreover we make contact with the Modified Newtonian Dynamics (MOND) approach for gravity by considering a particular ansatz for a given gauge field. We extend our results to a generalized non-relativistic MacDowell-Mansouri gravity theory by considering a generalized Newton-Hooke algebra.
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