  We discuss a mechanism through which the multi-vacua theories, such as String
Theory, could solve the Hierarchy Problem, without any UV-regulating physics at
low energies. Because of symmetry the number density of vacua with a certain
hierarchically-small Higgs mass diverges, and is an attractor on the vacuum
landscape.The hierarchy problem is solved in two steps. It is first promoted
into a problem of the super-selection rule among the infinite number of vacua
(analogous to theta-vacua in QCD), that are finely scanned by the Higgs mass.
This rule is lifted by heavy branes, which effectively convert the Higgs mass
into a dynamical variable. The key point is that a discrete
"brane-charge-conjugation" symmetry guarantees that the fineness of the
vacuum-scanning is set by the Higgs mass itself. On a resulting landscape in
all, but a measure-zero set of vacua the Higgs mass has a common
hierarchically-small value. In minimal models this value is controlled by the
QCD scale and is of the right magnitude. Although in each particular vacuum
there is no visible UV-regulating low energy physics, the realistic models are
predictive. For example, we show that in the minimal case the "charge
conjugation" symmetry is automatically a family symmetry, and imposes severe
restrictions on quark Yukawa matrices.
