The Thinker Musings

Depends what you mean.

Written in terms of a metric, GR is a theory with a local gauge symmetry (diffeomorphisms). Presumably, thought, what you want is something formulated as a theory of connections on a $G$-principal bundle, for some suitable choice of $G$.

That sorta works in 3 dimensions, as shown long ago, by Witten. The choice of $G$ depends both on the signature and the sign of the cosmological constant. For $\Lambda=0$ and Minkowski signature, $G$ is the Poincaré group, $G=ISO(2,1)$. The action is of Chern-Simons type.

Unfortunately:

1. That formulation is not easily coupled to dynamical matter.
2. The natural domain of integration for the gauge theory (as subsequent evidence has shown) is peculiar, and probably not what one wants, for a theory of gravity.

Those two comments are related.

In 4 dimensions, the best you can do is based on $G=SO(4,1)$. And similar criticisms hold (modulo the fact that one doesn’t have nearly the same control over the quantum theory, as in the 3D case).

All in all, this has not proven a terribly promising avenue. I think you should ask yourself what you hope the gauge theory point of view will buy you.