  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.
