Renormalisable Gravity, Dimensional Transmutation and Grand Unification

I consider prototype Grand Unified Theories consisting of scale invariant gauge theories coupled to renormalizable gravity. I show that such theories can be asymptotically free, and that dimensional transmutation (DT) can occur, both spontaneously breaking the gauge theory and inducing a Planck mass. Below the DT scale, the model takes the usual form of matter coupled to Einstein-Hilbert gravity in de Sitter space plus calculable corrections. Furthermore, the asymptotic
behavior of the coupling constants lie within the range of convergence of the Euclidean path integral. Although open questions remain concerning unitarity of all such renormalizable models of gravity, it is not obvious that, in curved backgrounds such as those considered here, unitarity is violated.

I will also make some brief remarks about historic beta-function calculations, the first order or Palantini formalism, and also the A-theorem and the possibility of applying this to renormalizable gravity.