# Ghost and tachyon free Poincar\'e gauge theories: a systematic approach

## TL;DR

This paper introduces a systematic, computer-implemented method to identify ghost- and tachyon-free parameter conditions in parity-preserving Poincaré gauge theories of gravity, revealing numerous stable and renormalizable models.

## Contribution

It develops a novel systematic approach, including a computer program, to analyze particle content and stability conditions in Poincaré gauge theories, uncovering many stable models with potential renormalizability.

## Key findings

- 450 ghost- and tachyon-free parameter cases identified
- 10 models are power-counting renormalizable
- 4 models have only massless propagating particles

## Abstract

A systematic method is presented for determining the conditions on the parameters in the action of a parity-preserving gauge theory of gravity for it to contain no ghost or tachyon particles. The technique naturally accommodates critical cases in which the parameter values lead to additional gauge invariances. The method is implemented as a computer program, and is used here to investigate the particle content of parity-conserving Poincar\'e gauge theory, which we compare with previous results in the literature. We find 450 critical cases that are free of ghosts and tachyons, and we further identify 10 of these that are also power-counting renormalizable, of which four have only massless tordion propagating particles and the remaining six have only a massive tordion propagating mode.