Black Holes and Large N Species Solution to the Hierarchy Problem

Understand

We provide the perturbative and non-perturbative arguments showing that theories with large number of species of the quantum fields, imply an inevitable hierarchy between the masses of the species and the Planck scale, shedding a different light on the hierarchy problem.

• In particular, using the black hole physics, we prove that any consistent theory that includes N number of the Z_2-conserved species of the quantum fields of mass \Lambda, puts a lower bound on the Planck mass, which in large N limit is given by N\Lambda^2.
• An useful byproduct of this proof is that any exactly conserved quantum charge, not associated with a long-range classical field, must be defined maximum modulo N, bounded by the the ratio of the Planck to the unit charge masses squared.
• For example, a continuous global U(1) `baryon number' symmetry, must be explicitly broken by gravity, at least down to a Z_N subgroup, with N bounded by the ratio of the Planck to baryon masses squared.