Eur. Phys. J. C (2017) 77: 249
https://doi.org/10.1140/epjc/s10052-017-4820-y

Regular Article - Theoretical Physics

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

¹ Instituto de Física, UFF-Universidade Federal Fluminense, Campus da Praia Vermelha, Av. General Milton Tavares de Souza s/n, Niterói, RJ, 24210-346, Brazil
² Departamento de Física Teórica, UERJ-Universidade Estadual do Rio de Janeiro, Rua São Francisco Xavier 524, Maracanã, Rio de Janeiro, RJ, 20550-013, Brazil
³ CBPF-Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, Rio de Janeiro, RJ, 22290-180, Brazil

^* e-mail: sobreiro@if.uff.br

Received: 21 December 2016
Accepted: 10 April 2017
Published online: 18 April 2017

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 of 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.