A conformal Model of Gravitons

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