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.

Chile

Luis Avilés

Patrick Concha

Spain

Javier Matulich

Evelyn Rodríguez

David Tempo

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

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.

Netherlands

Eric Bergshoeff

Octavio Fierro

Croatia

Jan Rosseel

A conformal approach to Carroll gravity

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.

Sebastián Salgado

3D Carrollian gravity from 2D Euclidean symmetry

<p>In this paper, we construct an exact solution of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></math> Einstein-Skyrme model in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo>=</mo><mn>4</mn></math> 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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> 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.</p>

Carla Henríquez-Baez

Marcela Lagos

Aldo Vera

Exact charged and rotating toroidal black hole in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> Einstein-Skyrme model

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 $$ \mathfrak{\max}$$ - $$ \mathfrak{bm}{\mathfrak{s}}_3 $$ algebra, which in turn corresponds the asymptotic symmetries of the Maxwell CS gravity. We also show that the $$ \mathfrak{h}{\mathfrak{s}}_3\mathfrak{\max} $$ - $$ \mathfrak{bm}{\mathfrak{s}}_3 $$ 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.

Daniel Pino

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

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.

Three-dimensional non-relativistic Hietarinta supergravity

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 AdS-Lorentz 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 <math><msub><mi>bms</mi><mn>3</mn></msub></math> 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-<math><msub><mi>bms</mi><mn>3</mn></msub></math> algebra, being the charge algebra of the minimal Maxwell supergravity theory in three dimensions.

Enlarged super-<math><mrow><msub><mrow><mi>bms</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> algebra and its flat limit

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   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 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 regimes.

Fernando Izaurieta

Four dimensional topological supergravities from transgression field theory

In this paper, we present a generalized 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  $$\left( p,q\right) $$  <math> <mfenced> <mi>p</mi> <mo>,</mo> <mi>q</mi> </mfenced> </math>   parameters. In particular, torsionless models are recovered for  $$q=0$$  <math> <mrow> <mi>q</mi> <mo>=</mo> <mn>0</mn> </mrow> </math>  .

Nelson Merino

Non-relativistic limit of the Mielke–Baekler gravity theory

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 super- $${{\mathfrak {bms}}}_{3}$$  <math> <msub> <mi>bms</mi> <mn>3</mn> </msub> </math>   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.