Unification of gauge and gravity Chern\u2013Simons theories in 3-D space-time

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 a 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.