# Effective Chern-Simons actions of particles coupled to 3D gravity

## TL;DR

This paper reviews and extends the derivation of effective Chern-Simons actions for particles in 3D gravity, exploring different isometry groups and their contractions, revealing novel particle dynamics and momentum space structures.

## Contribution

It introduces a new approach to derive effective particle actions for (anti-)de Sitter groups and explores the Carrollian particle description via group contractions.

## Key findings

- Effective actions for particles in 3D gravity can be derived from Chern-Simons theory.
- Group contractions lead to a Carrollian particle with AN(2) momentum space.
- The approach extends to multiple particles and different isometry groups.

## Abstract

Point particles in 3D gravity are known to behave as topological defects, while gravitational field can be expressed as the Chern-Simons theory of the appropriate local isometry group of spacetime. In the case of the Poincar\'e group, integrating out the gravitational degrees of freedom it is possible to obtain the effective action for particle dynamics. We review the known results, both for single and multiple particles, and attempt to extend this approach to the (anti-)de Sitter group, using the factorizations of isometry groups into the double product of the Lorentz group and AN(2) group. On the other hand, for the de Sitter group one can also perform a contraction to the semidirect product of AN(2) and the translation group. The corresponding effective action curiously describes a Carrollian particle with the AN(2) momentum space. We derive this contraction in a more rigorous manner and further explore its properties, including a generalization to the multiparticle case.