3D Carrollian gravity from 2D Euclidean symmetry

TL;DR

This paper develops Carrollian gravity models in three dimensions by applying Lie algebra expansion to 2D Euclidean algebras, leading to new non-relativistic gravity theories and their extensions.

Contribution

It introduces a systematic method to derive 3D Carrollian gravity models from 2D Euclidean symmetries using Lie algebra expansion, including novel algebraic structures and gravity theories.

Findings

Derived Carrollian gravity models in 3D from 2D Euclidean algebras.

Constructed Chern--Simons gravity theories based on these Carrollian algebras.

Connected the vanishing cosmological constant limit to a non-relativistic limit in 3D.

Abstract

Carroll symmetry arises from Poincar\'e 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.