Eur. Phys. J. C (2010) 67: 311-319
https://doi.org/10.1140/epjc/s10052-010-1297-3

Regular Article - Theoretical Physics

Discussing quantum aspects of higher-derivative 3-D gravity in the first-order formalism

¹ CBPF, Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180, Urca, Rio de Janeiro, Brazil
² Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Av. Governador Roberto Silveira, 1900, Prado, Nova Friburgo, Rio de Janeiro, Brazil
³ UFF, Universidade Federal Fluminense, Campus da Praia Vermelha, Av. Gal. Milton Tavares de Souza, s/nº, Niteroi, Rio de Janeiro, Brazil

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

Received: 4 February 2010
Published online: 30 March 2010

Abstract

In this paper, we reassess the issue of deriving the propagators and identifying the spectrum of excitations associated to the vielbein and spin connection of (1+2)-D gravity in the presence of dynamical torsion, while working in the first-order formulation. A number of peculiarities is pointed out whenever the Chern–Simons term is taken into account along with a combination of bilinear terms in the torsion tensor. We present a procedure to derive the full set of propagators, based on an algebra of enlarged spin-type operators, and we discuss under which conditions the poles of the tree-level 2-point functions correspond to physical excitations that do not conflict with causality and unitarity.