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

Abstract

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.

The gauging procedure and carrollian gravity

“…It has been argued that these symmetries need to be further enhanced by so-called dual supertranslations that arise most naturally from the first-order lagrangian (4.8) with the Holst term included [40,41]. Asymptotic symmetries of carrollian gravity were studied in [42,43]. It would be interesting to see whether the symmetries found in these works get additional contributions from the analogous terms in our carrollian lagrangians (5.19) and (6.2).…”

“…A better understanding of the equations of motion of the carrollian theories would therefore be of interest, cf. [11,12,25,42,43].…”

Magnetic Carrollian gravity from the Carroll algebra

“…There is another Carrollian contraction, called "magnetic" in [7], which is also easily obtained in the Hamiltonian formalism. Conserved charges and asymptotic symmetries for both "electric" and "magnetic" Carrollian gravity were then studied in [8][9][10]. 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.…”

Non-relativistic and ultra-relativistic expansions of three-dimensional spin-3 gravity theories

“…On one hand, non-relativistic symmetries appear in the context of holography [1][2][3][4][5][6][7][8][9][10][11][12], Hořava-Lifshitz gravity [13][14][15][16][17][18], effective field theory description of the quantum Hall effect [19][20][21][22][23], among others. On the other hand, ultra-relativistic symmetries of the Carrollian type have found recent applications in the study of tachyon JHEP10(2022)155 condensation [24], warped conformal field theories [25], tensionless strings [26][27][28][29][30], holography in asymptotically flat space-times [31][32][33][34][35][36][37][38], asymptotic symmetries [39][40][41] and in the context of soft hair on black hole horizons [42,43].…”