Black Holes and Large N Species Solution to the Hierarchy Problem

Abstract

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. The same constraint applies to any discrete gauge symmetry, as well as to other quantum-mechanically detectable black hole charges that are associated with the massive quantum hair of the black hole. We show that the gravitationally-coupled N-species sector that solves the gauge hirearchy problem, should be probed by LHC.