# Unification of Gauge and Gravity Chern-Simons Theories in 3-D Space time

## TL;DR

This paper demonstrates that by enlarging the gauge group, Chern-Simons gauge theory and gravity can be unified in 3D space-time, resulting in quantization conditions and a topological invariant.

## Contribution

It introduces a novel unification of Chern-Simons gauge theory and gravity in 3D by enlarging the gauge group, extending previous geometric approaches.

## Key findings

- Quantization of Chern-Simons coefficients for compact groups
- Unification leads to a topological invariant of 3D manifolds
- Unification does not quantize coefficients for non-compact groups

## Abstract

Chamseddine and Mukhanov showed that gravity and gauge theories could be unified in one geometric construction provided that a metricity condition is imposed on the vielbein. In this paper we are going to show that by enlarging the gauge group we are able to unify Chern-Simons gauge theory and Chern-Simons gravity in 3-D space-time. Such unification leads to the quantization of the coefficients for both Chern-Simons terms for compact groups but not for non-compact groups. Moreover, it leads to a topological invariant quantity of the 3 dimensional space-time manifold on which they are defined.