One Formulation for both Lineal Gravities through a Dimensional Reduction

TL;DR

This paper demonstrates that two different 1+1 dimensional linear gravities, based on de Sitter and Poincaré groups, can be derived from a single topological gauge theory via dimensional reduction of a 2+1 dimensional Chern--Simons model.

Contribution

It introduces a unified formulation for both gravities through a dimensional reduction of a 2+1D Chern--Simons theory, revealing their classical derivation from a common gauge framework.

Findings

Both gravities derive from a single topological gauge theory.

Dimensional reduction connects 2+1D Chern--Simons model to 1+1D gravity.

Unified gauge-theoretic origin for two distinct gravity models.

Abstract

The two lineal gravities --- based on the de Sitter group or a central extension of the Poincar\'e group in 1+1 dimensions --- are shown to derive classically from a unique topological gauge theory. This one is obtained after a dimensional reduction of a Chern--Simons model, which describes pure gravity in 2+1 dimensions, the gauge symmetry being given by an extension of ISO(2,1).