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It was recently found that, when linearised in the absence of matter, 58cases of the general gravitational theory with quadratic curvature and torsionare (i) free from ghosts and tachyons and (ii) power-counting renormalisable.We inspect the nonlinear Hamiltonian structure of the eight cases whose primaryconstraints do not depend on the curvature tensor. We confirm the particlespectra and unitarity of all these theories in the linear regime. We uncoverqualitative dynamical changes in the nonlinear regimes of all eight cases,suggesting at least a broken gauge symmetry, and possibly the activation ofnegative kinetic energy spin-parity sectors and acausal behaviour. Two of thecases propagate a pair of massless modes at the linear level, and wereinteresting as candidate theories of gravity. However, we identify these modeswith vector excitations, rather than the tensor polarisations of the graviton.Moreover, we show that these theories do not support a viable cosmologicalbackground.

Nonlinear Hamiltonian analysis of new quadratic torsion theories Part I. Cases with curvature-free constraints