Infrared foundations for quantum geometry. II. Catalog of all torsionlike theories including new ghost-tachyon-free cases

The construction of consistent effective field theories in the infrared suggests that models be defined by their underlying gauge symmetries, rather than by a tuning of couplings of operators which may not be stable against radiative corrections. Adhering to this principle, we systematically derive all linear, parity-conserving models that propagate a pair-antisymmetric rank-three field on a Minkowski background. Such models are relevant not only to torsion, but to many areas in high-energy physics ranging from dual graviton formulations to string theory and higher-spin theories. Starting from the general 12-parameter quadratic action, we obtain 206 gauge-symmetric specializations, of which 22 are free of ghosts and tachyons. Following this exhaustive classification, none of the unitary models are found to propagate scalar or pseudoscalar torsion, in stark contrast to the literature focus on spin-zero torsion. Instead, all models propagate one or more vector torsion modes.