3D gravity, point particles and deformed symmetries

TL;DR

This paper explores how 2+1 dimensional gravity, modeled as Chern-Simons theory with point particles as conical defects, leads to curved momentum space, especially in the presence of a cosmological constant.

Contribution

It investigates the effects of deformed symmetries and curved momentum space in 2+1D gravity with point particles, extending understanding to cases with non-zero cosmological constant.

Findings

Momentum space of particles is curved in 2+1D gravity.

Inclusion of cosmological constant affects the symmetry structure.

Effective particle actions reflect deformed symmetries.

Abstract

It is well known that gravity in 2+1 dimensions can be recast as Chern-Simons theory, with the gauge group given by the local isometry group, depending on the metric signature and the cosmological constant. Point particles are added into spacetime as (spinning) conical defects. Then, in principle, one may integrate out the gravitational degrees of freedom to obtain the effective particle action; the most interesting consequence is that the momentum space of a particle turns out to be curved. This is still not completely understood in the case of non-zero cosmological constant.