Power-counting renormalizable, ghost-and-tachyon-free Poincar\'e gauge theories

TL;DR

This paper identifies 48 new ghost- and tachyon-free Poincaré gauge theories of gravity that are power-counting renormalizable, expanding the known set and clarifying mode propagation and stability conditions.

Contribution

It extends the classification of critical, ghost-free, and renormalizable Poincaré gauge theories by presenting 48 new examples with detailed mode analysis.

Findings

48 new ghost- and tachyon-free critical PGT+ theories identified

Seven theories have 2 massless and one massive mode

Eight theories have only 2 massless modes, 33 have only massive modes

Abstract

We present 48 further examples, in addition to the 10 identified in [1], of ghost-and-tachyon-free critical cases of parity-conserving Poincar\'e gauge theories of gravity (PGT$^+$) that are also power-counting renormalizable (PCR). This is achieved by extending the range of critical cases considered. Of the new PCR theories, seven have 2 massless degrees of freedom (d.o.f.) in propagating modes and a massive $0^-$ or $2^-$ mode, eight have only 2 massless d.o.f., and 33 have only massive mode(s). We also clarify the treatment of nonpropagating modes in determining whether a theory is PCR.