Ghost- and tachyon-free Weyl gauge theories: A systematic approach

Abstract

We investigate the particle content of parity-preserving Weyl gauge theories of gravity (${\mathrm{WGT}}^{+}$) about a Minkowski background. Within a subset of the full theory, we use a systematic method previously presented by Lin et al. [Phys. Rev. D 99, 064001 (2019)] to determine 862 critical cases for which the parameter values in the action lead to changes of particle contents or additional gauge invariances. We find that 168 of these cases are free of ghosts and tachyons, provided the parameters satisfy certain conditions that we also determine. We further identify 40 of these cases that are also propagating power-counting renormalizable and determine the corresponding conditions on the parameters. Of these theories, 11 have only massless tordion propagating particles, 23 have only a massive tordion propagating mode, and 6 have both. We also repeat our analysis for ${\mathrm{WGT}}^{+}$ with vanishing torsion or curvature, respectively. We compare our findings with the very few previous results in the literature.