arXiv subjects

Sebastián Salgado

Publications and source records attributed to Sebastián Salgado.

5 recordsLinked to original sources

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 Lévy-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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arXiv2025

Extended Bargmann FDA and non-relativistic gravity

In this paper we consider the construction of a free differential algebra as an extension of the extended Bargmann algebra in arbitrary dimensions. This is achieved by introducing a new Maurer-Cartan equation for a three-form gauge multiplet in the adjoint representation of the extended Bargmann algebra. The new Maurer-Cartan equation is provided of non-triviality by means of the introduction of a four-form cocycle, representative of a Chevalley-Eilenberg cohomology class. We derive the corresponding dual $L_{\infty}$ algebra and, by using the formalism of non-linear realizations, propose a five-dimensional gauge invariant action principle. Then, we derive the corresponding equations of motion and study how the presence of the three-form gauge fields and the four-cocycle modify the corresponding non-relativistic dynamics.

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arXiv2024

3D Carrollian gravity from 2D Euclidean symmetry

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.

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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 $\mathcal{N}=1$ Poincaré 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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