Carrollian Perspective on Celestial Holography

Asymptotic symmetries of electric and magnetic Carrollian gravitational theories with a negative cosmological constant Λ are analyzed in 3+1 space-time dimensions. In the magnetic theory, the asymptotic symmetry algebra is given by the conformal Carroll algebra in three dimensions, which is infinite-dimensional and isomorphic to the BMS4 algebra. These results are in full agreement with holographic expectations, providing a new framework for the study of Carrollian holography. On the contrary, in the case of the electric theory, the presence of a negative Λ turns out to be incompatible with a consistent set of asymptotic conditions, that can be traced back to the absence of a sensible ground state configuration. This can be improved if the Carrollian theory obtained from an electric contraction of Euclidean General Relativity is considered. In this case, asymptotic conditions can be constructed with an asymptotic symmetry algebra given by so (1, 4). However, it is shown that the space of spherically symmetric solutions of this theory is degenerate.

Section: Jhep09(2022)044mentioning

confidence: 99%

Asymptotic symmetries in Carrollian theories of gravity with a negative cosmological constant

Pérez

2022

“…Aside from the original motivation, Carrollian field theories and gravity recently received a renewed interest due to their relation with the physics taking place at the null boundaries of asymptotically-flat spacetimes in general relativity, see e.g. [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Magnetic Carrollian gravity from the Carroll algebra

Campoleoni

Henneaux

Pekar

et al. 2022

“…Reasons to be interested in carrollian physics are plentiful, the most obvious one being its connection to null hypersurfaces in lorentzian spacetimes. Thus it plays a prominent rôle in the discussion of null infinity [13] (which in turn is connected to the celestial sphere [4,14,15]), black hole horizons [16] or spatial and timelike infinity [4,17]. Consequently, it has been argued to provide a natural starting point for the discussion of flat space holography, e.g., as discussed in [18] or using carrollian fluids in [19].…”

Section: Introductionmentioning

confidence: 99%

The gauging procedure and carrollian gravity

Figueroa-O’Farrill

Have

Prohazka

et al. 2022

We discuss a gauging procedure that allows us to construct lagrangians that dictate the dynamics of an underlying Cartan geometry. In a sense to be made precise in the paper, the starting datum in the gauging procedure is a Klein pair corresponding to a homogeneous space. What the gauging procedure amounts to is the construction of a Cartan geometry modelled on that Klein geometry, with the gauge field defining a Cartan connection. The lagrangian itself consists of all gauge-invariant top-forms constructed from the Cartan connection and its curvature. After demonstrating that this procedure produces four-dimensional General Relativity upon gauging Minkowski spacetime, we proceed to gauge all four-dimensional maximally symmetric carrollian spaces: Carroll, (anti-)de Sitter-Carroll and the lightcone. For the first three of these spaces, our lagrangians generalise earlier first-order lagrangians. The resulting theories of carrollian gravity all take the same form, which seems to be a manifestation of model mutation at the level of the lagrangians. The odd one out, the lightcone, is not reductive and this means that although the equations of motion take the same form as in the other cases, the geometric interpretation is different. For all carrollian theories of gravity we obtain analogues of the Gauss-Bonnet, Pontryagin and Nieh-Yan topological terms, as well as two additional terms that are intrinsically carrollian and seem to have no lorentzian counterpart. Since we gauge the theories from scratch this work also provides a no-go result for the electric carrollian theory in a first-order formulation.