  The discovery of the Higgs boson by the ATLAS and CMS collaborations allowed
us to precisely determine its mass being 125.09 $\pm$ 0.24GeV. This value is
intriguing as it lies at the frontier between the regions of stability and
meta-stability of the standard model vacuum. It is known that the hierarchy
problem can be interpreted in terms of the near criticality between the two
phases. The coefficient of the Higgs bilinear in the scalar potential, $m^{2}$,
is pushed by quantum corrections away from zero, towards the extremes of the
interval $[-M^{2}_{Pl},M^{2}_{Pl}]$ where $M_{Pl}$ is the Planck mass. In this
article, I show that demanding topological invariance for the renormalisation
group allows us to extend the beta functions such that the particular value of
the Higgs mass parameter observed in our universe regains naturalness. In
holographic terms, invariance to changes of topology in the bulk is dual to a
natural large hierarchy in the boundary quantum field theory. The demand of
invariance to topology changes in the bulk appears to be strongly tied to the
invariance of string theory to T-duality in the presence of H-fluxes.
