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

TL;DR

This paper analyzes the quantum properties of higher-derivative 3D gravity with torsion in the first-order formalism, focusing on propagator derivation and physical excitation spectrum, especially considering Chern-Simons contributions.

Contribution

It introduces a new method to derive propagators in 3D gravity with torsion, accounting for Chern-Simons terms and analyzing conditions for physical excitations.

Findings

Derived full set of propagators using algebra of spin operators

Identified conditions for physical poles consistent with causality

Analyzed effects of Chern-Simons term on spectrum

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.