Black holes and large N species solution to the hierarchy problem

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 A, must have a value of the Planck mass, which in large N limit is given by M(P)(2) greater than or similar to NA(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 Mp/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 less than or similar to (Mp/mb)(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. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinhcim