Equivalence between the Lovelock-Cartan action and a constrained gauge theory

TL;DR

This paper demonstrates that the four-dimensional Lovelock-Cartan gravitational action can be derived from a topological gauge theory with BRST symmetry, linking gravity to gauge theory frameworks without explicit metric dependence.

Contribution

It establishes an equivalence between the Lovelock-Cartan action and a constrained gauge theory, introducing the vierbein via BRST trivial constraints and identifying physical constants within the gauge framework.

Findings

Lovelock-Cartan action derived from gauge theory

Identification of Newton's constant with a mass parameter

Discussion on extending the model to quantum regime

Abstract

We show that the four-dimensional Lovelock-Cartan action can be derived from a massless gauge theory for the $SO(1,3)$ group with an additional BRST trivial part. The model is originally composed by a topological sector and a BRST exact piece and has no explicit dependence on the metric, the vierbein or a mass parameter. The vierbein is introduced together with a mass parameter through some BRST trivial constraints. The effect of the constraints is to identify the vierbein with some of the additional fields, transforming the original action into the Lovelock-Cartan one. In this scenario, the mass parameter is identified with Newton's constant while the gauge field is identified with the spin-connection. The symmetries of the model are also explored. Moreover, the extension of the model to a quantum version is qualitatively discussed.