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arXiv · 2501.00205

3D Carrollian gravity from 2D Euclidean symmetry

Patrick Concha·Evelyn Rodríguez·Sebastián Salgado
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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.

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Patrick Concha, Evelyn Rodríguez, Sebastián Salgado. 2024-12-31. 3D Carrollian gravity from 2D Euclidean symmetry. https://arxiv.org/abs/2501.00205

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