Scale-dependent Planck mass and Higgs VEV from holography and functional renormalization

We compute the scale-dependence of the Planck mass and of the vacuum expectation value of the Higgs field using two very different renormalization group methods: a 'holographic' procedure based on Einstein's equations in five dimensions with matter confined to a 3-brane, and a 'functional' procedure in four dimensions based on a Wilsonian momentum cutoff. Both calculations lead to very similar results, suggesting that the coupled theory approaches a non-trivial fixed point in the ultraviolet.