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 Z 2‐conserved species of the quantum fields of mass Λ, must have a value of the Planck mass, which in large N limit is given by M P2 \gsim N Λ 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, with N \gsim (M P/m)2, where m is the mass of the unit charge. 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 \lsim (M P/m b)2, where m b is the baryon mass. 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.