Biconformal Compactification

The gauging of the conformal group of n-dim Euclidean space by the homogenous Weyl group leads to a principal bundle known as biconformal space. Time arises naturally on a 2n-dimensional symplectic manifold with SO(n) spanning the fibers. These spaces allow a scale-invariant first-order gravity action, making them ideal candidates for quantizable gravity. We investigate the effect of including m compact dimensions beyond the 4 of spacetime. This gives 2m extra dimensions on the symplectic manifold that need to be compactified. Various compactifications lead to different fields, but for m=1,2 the set of compactifications is countable.