Deformed Carroll particle from 2+1 gravity

TL;DR

This paper explores how a point particle coupled to 2+1 gravity with a de Sitter gauge group leads to a deformed Carroll particle, revealing new contraction limits and their implications for particle dynamics.

Contribution

It introduces a novel contraction limit of the gauge group resulting in a deformed Carroll particle with de Sitter momentum space, expanding understanding beyond the Poincare case.

Findings

Identifies two contraction limits of the gauge group in 2+1 gravity.

Derives a deformed particle action with de Sitter momentum space.

Shows the mass shell constraint leads to a deformed Carroll particle.

Abstract

We consider a point particle coupled to 2+1 gravity, with de Sitter gauge group SO(3,1). We observe that there are two contraction limits of the gauge group: one resulting in the Poincare group, and the second with the gauge group having the form AN(2) \ltimes \an(2)^*. The former case was thoroughly discussed in the literature, while the latter leads to the deformed particle action with de Sitter momentum space, like in the case of kappa-Poincare particle. However, the construction forces the mass shell constraint to have the form p_0^2 = m^2, so that the effective particle action describes the deformed Carroll particle.