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Abstract We analyze SO(N) and SU(N) gauge theories with scalars in adjoint and fundamental representations, coupled to renormalisable, classically scale invariant gravity. In the specific case of SO(11), we show that the quantum field theory can be can be asymptotically free in all couplings (hence ultra-violet complete). For a region of parameter space, Dimensional Transmutation occurs, with the adjoint vacuum expectation value breaking SO(11) → SU(6) ⊗ U(1) and producing a Low Energy Effective Theory having Einstein-Hilbert gravity. We verify that certain minima are locally stable and lie within the catchment basin of the ultraviolet fixed points.