Dra. Rodríguez-Durán, Evelyn

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 ≤ 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.

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 N =2 supersymmetric extension of the Mielke-Baekler algebra and implementing a nonrelativistic 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.

Carroll symmetry arises from Poincaré 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.

In this paper, we construct an exact solution of the 𝑆⁢𝑈⁡(𝑁) Einstein-Skyrme model in 𝐷 =4 space-time dimensions describing a charged and rotating black hole with toroidal horizon. Rotation is added by applying an improper coordinate transformation to the known static toroidal black hole with Skyrme hair, while the electric charge is supplemented by considering a 𝑈⁡(1) gauge field interacting with Einstein gravity. We perform the thermal analysis in the grand canonical ensemble, explicitly showing the role that the flavor number plays. Some discussions about stability are also considered.

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 max-bms3 algebra, which in turn corresponds the asymptotic symmetries of the Maxwell CS gravity. We also show that the hs3max-bms3 algebra can alternatively be obtained as a vanishing cosmological constant limit of three copies of the algebra, with three independent central charges.

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 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.

We construct conformal Carroll geometry by gauging the conformal Carroll algebra. In doing so, we pay special attention to the way the so-called intrinsic torsion tensor components enter into the transformation rules of the geometric fields. As an application of our results, we couple a single electric/magnetic massless scalar to conformal Carroll gravity and show how, upon gauge-fixing the dilatations, we obtain a non-conformal version of electric/magnetic Carroll gravity.

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.

In this work, we classify all extended and generalized kinematical Lie algebras that can be obtained by expanding the 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-defned 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.

In this paper we present the Hietarinta Chern–Simons supergravity theory in three space-time dimensions which extends the simplest Poincaré 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 superbms3 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.