Chern-Simons Gravity with (Curvature)$^{2}$- and (Torsion)$^{2}$-Terms and A Basis of Degree-of-Freedom Projection Operators

TL;DR

This paper examines how (Curvature)^2- and (Torsion)^2-terms in a 3D gravity model affect unitarity and particle spectrum, demonstrating the utility of a new projection operator basis for propagator calculations.

Contribution

It introduces and validates an orthogonal basis of degree-of-freedom projection operators for analyzing parity-breaking gravity models in three dimensions.

Findings

Chern-Simons term does not affect unitarity conditions.

Chern-Simons term significantly alters the particle spectrum.

The projection operator basis is effective for propagator derivation.

Abstract

We investigate the effects of (Curvature)$^{2}$- and (Torsion)$^{2}$- terms in the Einstein-Hilbert-Chern-Simons Lagrangian. The purposes are two-fold: (i) to show the efficacy of an orthogonal basis of degree-of-freedom projection operators recently proposed and to ascertain its adequacy for obtaining propagators of general parity-breaking gravity models in three dimensions; (ii) to analyze the role of the topological Chern-Simons term for the unitarity and the particle spectrum of the model squared-curvature terms in connection with dynamical torsion. Our conclusion is that the Chern-Simons term does not influence the unitarity conditions imposed on the parameters of the Lagrangian, but significantly modifies the particle spectrum.