A conformal model of gravitons

In the description of general covariance, the vierbein and the Lorentz connection can be treated as independent fundamental fields. With the usual gauge Lagrangian, the Lorentz connection is characterized by an asymptotically free running coupling. When running from high energy, the coupling gets large at a scale which can be called the Planck mass. If the Lorentz connection is confined at that scale, the low energy theory can have the Einstein Lagrangian induced at low energy through dimensional transmutation. However, in general there will be new divergences in such a theory and the Lagrangian basis should be expanded. I construct a conformally invariant model with a larger basis size which potentially may have the same property.