Nonlinear Hamiltonian analysis of new quadratic torsion theories Part I.
  Cases with curvature-free constraints
  It was recently found that, when linearised in the absence of matter, 58
cases of the general gravitational theory with quadratic curvature and torsion
are (i) free from ghosts and tachyons and (ii) power-counting renormalisable.
We inspect the nonlinear Hamiltonian structure of the eight cases whose primary
constraints do not depend on the curvature tensor. We confirm the particle
spectra and unitarity of all these theories in the linear regime. We uncover
qualitative dynamical changes in the nonlinear regimes of all eight cases,
suggesting at least a broken gauge symmetry, and possibly the activation of
negative kinetic energy spin-parity sectors and acausal behaviour. Two of the
cases propagate a pair of massless modes at the linear level, and were
interesting as candidate theories of gravity. However, we identify these modes
with vector excitations, rather than the tensor polarisations of the graviton.
Moreover, we show that these theories do not support a viable cosmological
background.
