Black Holes and Large N Species Solution to the Hierarchy Problem

TL;DR

This paper introduces a large-$N$ species framework as a novel angle on the hierarchy problem, deriving a fundamental bound $M_P^2 \gtrsim N\Lambda^2$ from both perturbative graviton renormalization and non-perturbative black hole physics (up to $\ln N$ corrections). It shows that gravity effectively weakens by $1/N$ in the presence of many fields of mass $\Lambda$, and explores two realizations: a huge number of species or a large $Z_N$ symmetry, with broad implications for conserved quantum numbers, discrete/global symmetry breaking, and black hole quantum hair. The work also argues that any such hidden sector would be accessible at the LHC through gravitationally suppressed but collectively enhanced couplings, making this scenario experimentally testable. It connects to broader themes like massive spin-2 hair, charge quantization, and potential links to string theory landscapes with many light states. Overall, the paper presents a coherent non-perturbative mechanism to address the hierarchy problem and outlines concrete phenomenological expectations for collider experiments.

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 Λ, puts a lower bound on the Planck mass, which in large N limit is given by NΛ^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.