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We analyze $SO(N)$ and $SU(N)$ gauge theories with scalars in adjoint andfundamental representations, coupled to renormalisable, classically scaleinvariant gravity. In the specific case of $SO(12),$ we show that the quantumfield theory can be can be asymptotically free in all couplings (henceultra-violet complete). For a region of parameter space, DimensionalTransmutation occurs, with the adjoint vacuum expectation value breaking$SO(12) \to SU(6)\otimes U(1)$ and producing a Low Energy Effective Theoryhaving Einstein-Hilbert gravity. We verify that certain minima are locallystable and lie within the catchment basin of the ultraviolet fixed points.

Grand Unified Theories in Renormalisable, Classically Scale Invariant Gravity