Discussing Quantum Aspects of Higher-Derivative 3D-Gravity in the First-Order Formalism

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.