Remarks on Quantum Aspects of 3D-Gravity in the First-Order Formalism

TL;DR

This paper analyzes the quantum properties of 3D gravity in the first-order formalism, focusing on propagators, spectrum, and the effects of torsion and Chern-Simons terms.

Contribution

It introduces a method to derive propagators and identify physical excitations in 3D gravity with torsion, considering the impact of Chern-Simons terms.

Findings

Derived full set of propagators using spin-type operators

Identified conditions for physical excitations in the spectrum

Discussed peculiarities introduced by Chern-Simons and torsion terms

Abstract

In this paper, we reassess the issue of working out the propagators and identifying the spectrum of excitations associated to the vielbein and spin connection of (1+2)-D gravity in the presence of torsion by adopting the first-order formulation. A number of peculiarities is pointed out whenever the Chern-Simons term is taken into account along with the possible bilinear terms in the torsion tensor. We present a procedure to derive the full set of propagators, based on a set of spin-type operators, and we discuss under which conditions the pole of these tree-level 2-point functions correspond to physical excitations.