arXiv subjects

Patrick Concha

Publications and source records attributed to Patrick Concha.

At least 37 records · Page 2Linked to original sources

arXiv2022

Three-dimensional Newtonian gravity with cosmological constant and torsion

In this paper we present an alternative cosmological extension of the three-dimensional extended Newtonian Chern-Simons gravity by switching on the torsion. The theory is obtained as a non-relativistic limit of an enhancement and $U(1)$-enlargement of the so-called teleparallel algebra and can be seen as the teleparallel analogue of the Newtonian gravity theory. The infinite-dimensional extension of our result is also explored through the Lie algebra expansion method. An infinite-dimensional torsional Galilean gravity model is presented which in the vanishing cosmological constant limit reproduces the infinite-dimensional extension of the Galilean gravity theory.

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arXiv2021

Three-dimensional non-relativistic supergravity and torsion

In this paper we present a torsional non-relativistic Chern-Simons teleparallel (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 $\mathcal{N}=2$ 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.

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arXiv2021

Three-dimensional Maxwellian Carroll gravity theory and the cosmological constant

In this work, we present the three-dimensional Maxwell Carroll gravity by considering the ultra-relativistic limit of the Maxwell Chern-Simons gravity theory defined in three spacetime dimensions. We show that an extension of the Maxwellian Carroll symmetry is necessary in order for the invariant tensor of the ultra-relativistic Maxwellian algebra to be non-degenerate. Consequently, we discuss the origin of the aforementioned algebra and theory as a flat limit. We show that the theoretical setup with cosmological constant yielding the extended Maxwellian Carroll Chern-Simons gravity in the vanishing cosmological constant limit is based on an enlarged extended version of the Carroll symmetry. Indeed, the latter exhibits a non-degenerate invariant tensor allowing the proper construction of a Chern-Simons gravity theory which reproduces the extended Maxwellian Carroll gravity in the flat limit.

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arXiv2021

Hypersymmetric extensions of Maxwell Chern-Simons gravity in (2+1) dimensions

We present a consistent way of coupling three-dimensional Maxwell Chern-Simons gravity theory with massless spin-$\frac{5}{2}$ gauge fields. We first introduce the simplest hyper-Maxwell Chern-Simons gravity containing two massless spin-2 fields coupled with a massless Majorana fermion of spin-$\frac{5}{2}$ and whose novel underlying superalgebra is explicitly constructed. Then, we present three alternative hypersymmetric extensions of the Maxwell algebra which are shown to emerge from the Inönü-Wigner contraction procedure of precise combinations of the $\mathfrak{osp}\left(1|4\right)$ and the $\mathfrak{sp}\left(4\right)$ algebras. This allow us to construct distinct types of hyper-Maxwell Chern-Simons theories that extend to include generically interacting non-propagating spin-$4$ fields accompanied by one or two spin-$\frac{5}{2}$ gauge fields.

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arXiv2021

Three-dimensional exotic Newtonian supergravity theory with cosmological constant

We present a supersymmetric extension of the exotic Newtonian Chern-Simons gravity theory in three spacetime dimensions. The underlying new non-relativistic superalgebra is obtained by expanding the $\mathcal{N}=2$ AdS superalgebra and can be written as two copies of the enhanced Nappi-Witten algebra, one of which is augmented by supersymmetry. We show that the exotic Newtonian superalgebra allows to introduce a cosmological constant to the extended Newtonian supergravity. Interestingly, the obtained supergravity action contains the extended Newton-Hooke supergravity as a sub-case.

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arXiv2021

Three-dimensional teleparallel Chern-Simons supergravity theory

In this work we present a gauge-invariant three-dimensional teleparallel supergravity theory using the Chern-Simons 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 $\mathcal{N}=p+q$ supersymmetries is also explored.

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arXiv2020

Non-relativistic three-dimensional supergravity theories and semigroup expansion method

In this work we present an alternative method to construct diverse non-relativistic Chern-Simons supergravity theories in three spacetime dimensions. To this end, we apply the Lie algebra expansion method based on semigroups to a supersymmetric extension of the Nappi-Witten algebra. Two different families of non-relativistic superalgebras are obtained, corresponding to generalizations of the extended Bargmann superalgebra and extended Newton-Hooke superalgebra, respectively. The expansion method considered here allows to obtain known and new non-relativistic supergravity models in a systematic way. In particular, it immediately provides an invariant tensor for the expanded superalgebra, which is essential to construct the corresponding Chern-Simons supergravity action. We show that the extended Bargmann supergravity and its Maxwellian generalization appear as particular subcases of a generalized extended Bargmann supergravity theory. In addition, we demonstrate that the generalized extended Bargmann and generalized extended Newton-Hooke supergravity families are related through a contraction process.

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arXiv2020

Three-dimensional Maxwellian Extended Newtonian gravity and flat limit

In the present work we find novel Newtonian gravity models in three spacetime dimensions. We first present a Maxwellian version of the extended Newtonian gravity, which is obtained as the non-relativistic limit of a particular $U(1)$-enlargement of an enhanced Maxwell Chern-Simons gravity. We show that the extended Newtonian gravity appears as a particular sub-case. Then, the introduction of a cosmological constant to the Maxwellian extended Newtonian theory is also explored. To this purpose, we consider the non-relativistic limit of an enlarged symmetry. An alternative method to obtain our results is presented by applying the semigroup expansion method to the enhanced Nappi-Witten algebra. The advantages of considering the Lie algebra expansion procedure is also discussed.

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arXiv2020

Three-dimensional non-relativistic extended supergravity with cosmological constant

In this paper, we present novel non-relativistic superalgebras which correspond to supersymmetric extensions of the enlarged extended Bargmann algebra. The three-dimensional non-relativistic Chern-Simons supergravity actions invariant under the aforementioned superalgebras are constructed. The new non-relativistic superalgebras allow to accommodate a cosmological constant in a non-relativistic supergravity theory. Interestingly, we show that one of the non-relativistic supergravity theories presented here leads to the recently introduced Maxwellian exotic Bargmann supergravity when the flat limit $\ell \rightarrow\infty$ is considered. Besides, we show that both descriptions can be written in terms of a supersymmetric extension of the Nappi-Witten algebra or the extended Newton-Hooke superalgebra.

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arXiv2020

Generalized Maxwellian exotic Bargmann gravity theory in three spacetime dimensions

We present a generalization of the so-called Maxwellian extended Bargmann algebra by considering a non-relativistic limit to a generalized Maxwell algebra defined in three spacetime dimensions. The non-relativistic Chern-Simons gravity theory based on this new algebra is also constructed and discussed. We point out that the extended Bargmann and its Maxwellian generalization are particular sub-cases of the generalized Maxwellian extended Bargmann gravity introduced here. The extension of our results using the semigroup expansion method is also discussed.

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arXiv2020

Resonant superalgebras and $\mathcal{N}=1$ supergravity theories in three spacetime dimensions

We explore $\mathcal{N}=1$ supersymmetric 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 $Q_α$ concerning the so-called resonant algebras being characterized by the presence of an additional bosonic generator $Z_{a}$, besides the Lorentz $J_{a}$ and translation $P_{a}$ generators. Obtained eight supersymmetric $JPZ+Q$ schemes result directly from obeying super-Jacobi identities. We point out particular requirements that superalgebras have to satisfy to be successfully incorporated within valid supergravity actions. The presented algebraic and Lagrangian framework organizes and helps us better understand relations between the various supergravity and supersymmetric Chern-Simons actions invariant under diverse resonant superalgebras.

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arXiv2020

Three-dimensional Maxwellian extended Bargmann supergravity

We present a novel three-dimensional non-relativistic Chern-Simons supergravity theory invariant under a Maxwellian extended Bargmann superalgebra. We first study the non-relativistic limits of the minimal and the $\mathcal{N}=2$ 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.

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arXiv2020

Three-dimensional exotic Newtonian gravity with cosmological constant

In this work we introduce a cosmological constant in the extended Newtonian gravity theory. To this end, we extend the exotic Newton-Hooke algebra by introducing new generators and central charges. The new algebra obtained here has been denoted as exotic Newtonian algebra and reproduces the extended Newtonian one in the flat limit $\ell\rightarrow\infty$. A three-dimensional Chern-Simons action for the exotic Newtonian algebra is presented. We show that the non-relativistic gravity theory proposed here reproduces the most general extended Newtonian gravity theory in the flat limit.

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arXiv2019

On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions

In this work we obtain known and new supersymmetric extensions of diverse asymptotic symmetries defined in three spacetime dimensions by considering the semigroup expansion method. The super-$BMS_3$, the superconformal algebra and new infinite-dimensional superalgebras are obtained by expanding the super-Virasoro algebra. The new superalgebras obtained are supersymmetric extensions of the asymptotic algebras of the Maxwell and the $\mathfrak{so}(2,2)\oplus\mathfrak{so}(2,1)$ gravity theories. We extend our results to the $\mathcal{N}=2$ and $\mathcal{N}=4$ cases and find that R-symmetry generators are required. We also show that the new infinite-dimensional structures are related through a flat limit $\ell \rightarrow \infty$.

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arXiv2019

Non-Relativistic Gravity Theory based on an Enlargement of the Extended Bargmann Algebra

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 $\ell \rightarrow \infty$ 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.

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arXiv2019

Three-dimensional Poincaré supergravity and $\mathcal{N}$-extended supersymmetric BMS$_{3}$ algebra

A new approach for obtaining the three-dimensional Chern-Simons supergravity for the Poincaré algebra is presented. The $\mathcal{N}$-extended Poincaré supergravity is obtained by expanding the super Lorentz theory. We extend our procedure to their respective asymptotic symmetries and show that the $\mathcal{N}=(1,2,4)$ super-BMS$_{3}$ appear as expansions of one Virasoro superalgebra. Interestingly, the $\mathcal{N}$-extended super-BMS$_{3}$ obtained here are not only centrally extended but also endowed with internal symmetry. We also show that the $\mathcal{N}$-extended super Poincaré algebras with both central and automorphism generators are finite subalgebras.

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arXiv2019

$\mathcal{N}$-extended Maxwell supergravities as Chern-Simons theories in three spacetime dimensions

We present a new class of three-dimensional $\mathcal{N}$-extended supergravity theories based on the $\mathcal{N}$-extended Maxwell superalgebra with central charges and $\mathfrak{so}(\mathcal{N})$ internal symmetry generators. The presence of $\mathfrak{so}(\mathcal{N})$ generators is required in order to define a non-degenerate invariant inner product. Such symmetry allows us to construct an alternative supergravity action without cosmological constant term. Interestingly, the new theories can be obtained as a flat limit of a $\mathcal{N}$-extended AdS-Lorentz supergravity theories enlarged with $\mathfrak{so}(\mathcal{N})$ gauge fields.

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arXiv2019

Semi-simple enlargement of the $\mathfrak{bms}_3$ algebra from a $\mathfrak{so}(2,2)\oplus\mathfrak{so}(2,1)$ Chern-Simons theory

In this work we present a BMS-like ansatz for a Chern-Simons theory based on the semi-simple enlargement of the Poincaré symmetry, also known as AdS-Lorentz algebra. We start by showing that this ansatz is general enough to contain all the relevant stationary solutions of this theory and provides with suitable boundary conditions for the corresponding gauge connection. We find an explicit realization of the asymptotic symmetry at null infinity, which defines a semi-simple enlargement of the $\mathfrak{bms}_3$ algebra and turns out to be isomorphic to three copies of the Virasoro algebra. The flat limit of the theory is discussed at the level of the action, field equations, solutions and asymptotic symmetry.

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