arXiv subjects

Patrick Concha

Publications and source records attributed to Patrick Concha.

At least 19 recordsLinked to original sources

arXiv2026

Non-Relativistic Chern-Simons Supergravity with Torsion

In this work, we construct a three-dimensional non-relativistic Chern--Simons supergravity theory with both curvature and torsion within the Mielke--Baekler framework. We show that a consistent non-relativistic supergravity formulation requires starting from a $\mathcal{N}=2$ supersymmetric extension of the Mielke--Baekler algebra and implementing a non-relativistic expansion via the semigroup expansion method, rather than a naive contraction. This procedure allows one to overcome the usual difficulties of non-relativistic supergravity constructions, ensuring closure of the superalgebra and the existence of a non-degenerate invariant bilinear form. The resulting model is characterized by two parameters $(p,q)$, which interpolate between different non-relativistic supergravity theories, including the extended Bargmann, Newton--Hooke, and torsional models. Our results provide a unified framework for non-relativistic supergravity with torsion and open new avenues for exploring supersymmetric extensions of Galilean and Carrollian gravity theories.

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arXiv2026

Maxwell kinematical algebras and 3D gravities

In this paper, we present a Maxwell extension of kinematical Lie algebras by promoting the contraction method underlying the Bacry and L\'evy-Leblond cube to a semigroup expansion framework. Within this approach, we show that both non- and ultra-relativistic Maxwell algebras admitting non-degenerate invariant bilinear forms can be systematically obtained from different parent algebras through a unified expansion scheme, leading to a Maxwellian kinematical cube. This construction is further generalized to an infinite hierarchy of kinematical algebras. The expansion method naturally provides the corresponding invariant tensors, allowing for the systematic construction of three-dimensional Chern-Simons gravity theories.

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arXiv2026

Applied foliated conformal Carroll symmetries

We apply the conformal compensating technique for constructing matter couplings to conformal scalars on a $D$-dimensional foliated conformal Carroll manifold dividing the tangent space into $(p+1)$-dimensional longitudinal and $(D-p-1)$-dimensional transversal directions corresponding to $p$-branes. We show that the conformal Carroll algebra that was used for particle-like foliated geometries with $p=0$ cannot be used for higher-dimensional objects, called $p$-branes, with $0 < p \le D-2$. Furthermore, string-like foliated geometries are not suitable for the conformal compensating technique due to the conformal invariance in the longitudinal directions that is present for $p=1$. All other cases can be dealt with provided one uses a different conformal extension of the Carroll algebra that amounts to a conformal extension in the longitudinal directions only supplemented with an additional an-isotropic dilatation. By brane-duality similar results hold for foliated Galilean geometries which we present as well. Our results nicely fit in with recent work on foliated Aristotelian geometries.

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arXiv2025

Maxwell Chern-Simons gravity in 3D: Thermodynamics of cosmological solutions and black holes with torsion

We construct generalized sets of asymptotic conditions for both three-dimensional Maxwell Chern-Simons gravity and a novel extension that incorporates torsion through a deformation of the Maxwell algebra. These boundary conditions include the most general temporal components of the gauge fields that consistently preserve the corresponding asymptotic Maxwell algebras with identical classical central charges, while allowing for the inclusion of chemical potentials conjugate to the conserved charges. We show that both sets of asymptotic configurations admit nontrivial solutions carrying not only mass and angular momentum but also an additional global spin-2 charge. In the torsionless case, the theory admits locally flat cosmological spacetimes, whereas in the presence of torsion, it generalizes to BTZ-like black hole geometries. For each case, the thermodynamic properties are consistently derived in terms of the gauge fields and the topology of the Euclidean manifold, shown to correspond to a solid torus. Furthermore, we obtain a general expression for the entropy, depending on both the horizon area and its spin-2 analogues, which can be written as a reparametrization-invariant integral of the induced spin-2 fields on the spacelike section of the horizon.

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arXiv2024

3D Carrollian gravity from 2D Euclidean symmetry

Carroll symmetry arises from Poincar\'e symmetry when the speed of light is sent to zero. In this work, we apply the Lie algebra expansion method to find the Carroll versions of different gravity models in three space-time dimensions. Our starting point is the 2D Euclidean AdS algebra along with its flat version. Novel and already known Carrollian algebras, such as the AdS-Carroll and Carroll-Galilei ones are found, and the Chern--Simons gravity theories based on them are constructed. Remarkably, after the expansion, the vanishing cosmological constant limit applied to the 2D Euclidean AdS algebra converts into a non-relativistic limit in three space-time dimensions. We extend our results to Post-Carroll-Newtonian algebras which can be found by expanding a family of 2D Euclidean algebras.

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arXiv2024

A Conformal Approach to Carroll Gravity

We show how to take the first step in the conformal program for constructing general matter couplings to Carroll gravity. In particular, we couple a single massless electric/magnetic scalar to conformal Carroll gravity with isotropic dilatations and show how, upon gauge-fixing, we obtain a (non-conformal version of) electric/magnetic Carroll gravity. We determine the full Carroll transformation rules paying special attention to the way the so-called intrinsic torsion tensors occur in these transformation rules. A noteworthy feature in the magnetic case is that the Lagrange multiplier present in the Lagrangian gets absorbed, after coupling to conformal Carroll gravity and gauge-fixing, into one of the independent spin-connections of magnetic Carroll gravity. Our results form a convenient starting point for constructing general matter couplings to Carroll gravity. Surprisingly, we find that the same relation between dynamical matter and gravity, which forms the basis of the conformal program, does not work in the usual way in the Galilei case.

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arXiv2024

Non-Lorentzian Supergravity and Kinematical Superalgebras

In this paper, we present and classify the supersymmetric extensions of extended kinematical algebras, at the basis of non-Lorentzian physics theories. The diverse kinematical superalgebras are here derived by applying non- and ultra-relativistic expansion procedures involving different semigroups. We then build three-dimensional Chern-Simons non-Lorentzian supergravity theories based on such (extended) kinematical superalgebras, providing the supersymmetry transformation laws of the fields and the field equations of the models, which correspond to the vanishing of the curvature two-forms. In fact, the expansion procedure adopted allows to automatically end up with a non-degenerate bilinear invariant trace for the (extended) kinematical superalgebras. The latter is a crucial ingredient of the Chern-Simons field-theoretical formulation, as it allows to include a kinetic term for each gauge field of the theory, implying the vanishing of the curvature two-forms as field equations.

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arXiv2024

Asymptotic structure of three-dimensional Maxwell Chern-Simons gravity coupled to spin-3 fields

In this work we analyze the asymptotic symmetries of the three-dimensional Chern-Simons (CS) gravity theory for a higher spin extension of the so-called Maxwell algebra. We propose a generalized set of asymptotic boundary conditions for the aforementioned flat gravity theory and we show that the corresponding charge algebra defines a higher-spin extension of the $\mathfrak{max}$-$\mathfrak{bms}_{3}$ algebra, which in turn corresponds the asymptotic symmetries of the Maxwell CS gravity. We also show that the $\mathfrak{hs}_3\mathfrak{max}$-$\mathfrak{bms}_{3}$ algebra can alternatively be obtained as a vanishing cosmological constant limit of three copies of the $\mathcal{W}_3$ algebra, with three independent central charges.

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arXiv2024

Three-dimensional non-relativistic Hietarinta supergravity

In this work we present the non-relativistic regime of the Hietarinta gravity theory and its extension to supergravity. At the bosonic level, we derive the non-relativistic version of the Hietarinta model by employing a contraction process and addressing the non-degeneracy of the invariant metric. To incorporate supersymmetry, we apply the Lie algebra expansion method to obtain the non-relativistic formulation of $\mathcal{N}=2$ Hietarinta supergravity. Our results reveal that the non-relativistic Hietarinta theory encompasses the extended Bargmann (super)gravity as a special case, yet it differs significantly from other existing non-relativistic (super)gravity models. Furthermore, we generalize our analysis to include a cosmological constant term in the non-relativistic Hietarinta (super)gravity action and examine its effects on the torsion structure.

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arXiv2023

Four dimensional topological supergravities from transgression field theory

In this work, we propose a four-dimensional gauged Wess-Zumino-Witten model, obtained as a dimensional reduction from a transgression field theory invariant under the $\mathcal{N}=1$ Poincar\'{e} supergroup. For this purpose, we consider that the two gauge connections on which the transgression action principle depends are given by linear and non-linear realizations of the gauge group respectively. The field content of the resulting four-dimensional theory is given by the gauge fields of the linear connection, in addition to a set of scalar and spinor multiplets in the same representation of the gauge supergroup, which in turn, correspond to the coordinates of the coset space between the gauge group and the five-dimensional Lorentz group. We then decompose the action in terms of four-dimensional quantities and derive the corresponding equations of motion. We extend our analysis to the non- and ultra- relativistic regime.

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arXiv2023

Hietarinta Chern-Simons supergravity and its asymptotic structure

In this paper we present the Hietarinta Chern-Simons supergravity theory in three space-time dimensions which extends the simplest Poincar\'e supergravity theory. After approaching the construction of the action using the Chern-Simons formalism, the analysis of the corresponding asymptotic symmetry algebra is considered. For this purpose, we first propose a consistent set of asymptotic boundary conditions for the aforementioned supergravity theory whose underlying symmetry corresponds to the supersymmetric extension of the Hietarinta algebra. We then show that the corresponding charge algebra contains the super-$\mathfrak{bms}_{3}$ algebra as subalgebra, and has three independent central charges. We also show that the obtained asymptotic symmetry algebra can alternatively be recovered as a vanishing cosmological constant limit of three copies of the Virasoro algebra, one of which is augmented by supersymmetry.

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arXiv2023

Extended Kinematical 3D Gravity Theories

In this work, we classify all extended and generalized kinematical Lie algebras that can be obtained by expanding the $\mathfrak{so}\left(2,2\right)$ 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.

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arXiv2023

Non-relativistic limit of the Mielke-Baekler gravity theory

In this paper, we present the most general non-relativistic 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 $\left(p,q\right)$ parameters. In particular, torsionless models are recovered for $q=0$.

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arXiv2023

Three-dimensional Hypergravity Theories and Semigroup Expansion Method

In this work we present novel and known three-dimensional hypergravity theories which are obtained by applying the powerful semigroup expansion method. We show that the expansion procedure considered here yields a consistent way of coupling different three-dimensional Chern-Simons gravity theories with massless spin-$\frac{5}{2}$ gauge fields. First, by expanding the $\mathfrak{osp}\left(1|4\right)$ superalgebra with a particular semigroup a generalized hyper-Poincar\'e algebra is found. Interestingly, the hyper-Poincar\'e and hyper-Maxwell algebras appear as subalgebras of this generalized hypersymmetry algebra. Then, we show that the generalized hyper-Poincar\'e CS gravity action can be written as a sum of diverse hypergravity CS Lagrangians. We extend our study to a generalized hyper-AdS gravity theory by considering a different semigroup. Both generalized hyperalgebras are then found to be related through an In\"on\"u-Wigner contraction which can be seen as a generalization of the existing vanishing cosmological constant limit between the hyper-AdS and hyper-Poincar\'e gravity theories.

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arXiv2023

Exact flavored black $p$-branes and self-gravitating instantons from toroidal black holes with Skyrme hair

In this paper, using the maximal embedding of $SU(2)$ into $SU(N)$ in the Euler angles parameterization, we construct a novel family of exact solutions of the Einstein $SU(N)$-Skyrme model. First, we present a hairy toroidal black hole in $D=4$ dimensions. This solution is asymptotically locally anti-de Sitter and is characterized by discrete hair parameters. Then, we perform a dimensional extension of the black hole to obtain black $p$-branes as solutions of the Einstein $SU(N)$-Non-linear sigma model in $D\geq5$ dimensions. These are homogeneous and topologically protected. Finally we show that, through a Wick rotation of the toroidal black hole, one can construct an exact self-gravitating instanton. The role that the flavor number $N$ plays in the geometry and thermodynamics of these configurations is also discussed.

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arXiv2022

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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arXiv2022

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.

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arXiv2022

Phase transitions for charged planar solitons in AdS

In this work we study the phase transitions between the planar charged AdS black hole and the planar charged soliton. The planar soliton is obtained as a double analytic continuation of the charged black hole metric, which also involves analytically continuing the electric charge. We show that there are phase transitions between both solutions depending on the electric potential, magnetic flux and temperature. The analysis is carried out in the Grand-Canonical ensemble.

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