Pure spin connection formulation of General Relativity and unification

I will discuss a new formulation of General Relativity that involves no metric field (or vierbein), but rather only the gauge field of the Lorentz group that is the spin connection. An interesting aspect of such a gauge-theoretical description is that it could serve as a starting point for unifying gravity with the other forces of the Standard Model by simply extending the Lorentz group. There are, however, important issues that obstruct such a simple picture and I will discuss some possible ways of dealing with them.