https://doi.org/10.1140/epjc/s10052-025-14234-6
Regular Article - Theoretical Physics
3D Carrollian gravity from 2D Euclidean symmetry
1
Departamento de Matemática y Física Aplicadas, Universidad Católica de la Santísima Concepción, Alonso de Ribera 2850, Concepción, Chile
2
Grupo de Investigación en Física Teórica, GIFT, Universidad Católica de la Santísima Concepción, Alonso de Ribera 2850, Concepción, Chile
3
Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile
a
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Received:
27
December
2024
Accepted:
27
April
2025
Published online:
11
May
2025
Abstract
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.
© The Author(s) 2025
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