Black holes and large N species solution to the hierarchy problem

By G. Dvali. 2007

545 citations recorded by the source corpus.

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 Z2‐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 MP2 \gsim N Λ2. 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 (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 ZN subgroup, with N \lsim (MP/mb)2, where mb 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/859776b753b186a63ca67b3b662642d226001019

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Citations in the corpus

Quantum extremal islands made easy. Part I. Entanglement on the brane (2020, background): “While the above are UV effects, there are also IR effects resulting from having a large number of matter degrees of freedom propagating on the brane, as explained in [84–86].”
A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices (2011, background): “There are several different claims that in order for the GSL to be true, certain restrictions must hold even semiclassically on e.g. bounds on the entropy and/or number of particle species proposed by Bekenstein [5], Bousso [6], or Dvali [7], bounds on the fine structure constant [8], the unbrokenne”
The Swampland: Introduction and Review (2019, background): “There is also an argument which follows if we require a black hole to fully discharge a discrete gauge symmetry [20], which fits in with this section.”
Quantum break-time of de Sitter (2017, background): “Currently, the phenomenologically acceptable number of hidden sector species is bounded by Nsp ∼ 1032 because a larger number of species would lower the gravity cutoff below the TeV-scale, which is excluded by current collider data [20].”
Evidence for a sublattice weak gravity conjecture (2016, background): “The idea of realizing a Z/(3 ) symmetry with N scalar fields coupled as φ†iφ 3 i+1 appeared already in [51].”
On the possibility of large axion moduli spaces (2014, background): “If anything, increasing the number of species will make a super-Planckian traversal more difficult, as the many scalar fields will lead to a sizeable renormalization of the Planck mass [12, 37].”
Black hole's quantum N‐portrait (2011, background): “In [5] it was shown that in the semi-classical treatment Nspecies sets an universal lower bound on the size of a smallest possible semi-classical black hole, LN , as,”
Lectures on the Swampland Program in String Compactifications (2021, background): “The same species bound has been motivated using non-perturbative arguments based on black hole physics [36,37].”
TASI Lectures on the Strong CP Problem and Axions (2018, background): “Although these approaches have been around for a long time [64, 65], a move of marketing genius has recently renamed them as clockwork models [66, 67].”
Black hole bound on the number of species and quantum gravity at CERN LHC (2007, unknown): “An example of such a consistency bound, was proved recently in [ 1 ].”
Quantum compositeness of gravity: black holes, AdS and inflation (2013, background): “In this respect, the situation with the de Sitter limit is similar to the depletion of black holes in the presence of large number of massless particle species [27].”
Black holeʼs 1/N hair (2012, methodology): “A similar argument was made quantitative and was used to put a bound on dimensionality of maximal representation of the global symmetry group in [9, 10].”