Infinite statistics, symmetry breaking and combinatorial hierarchy

TL;DR

This paper explores how infinite (quantum Boltzmann) statistics, or quons, can lead to a natural resolution of the hierarchy problem by allowing the Planck mass to be factorially larger than the cutoff, without fine-tuning.

Contribution

It introduces a novel approach where infinite statistics replaces Bose/Fermi statistics in high-energy theories, providing a new perspective on hierarchy problem resolution.

Findings

Infinite statistics can exponentially increase the effective Planck mass.

A quantum model demonstrating the hierarchy problem solution is presented.

The approach removes the need for artificially large parameters in fundamental theories.

Abstract

The physics of symmetry breaking in theories with strongly interacting quanta obeying infinite (quantum Boltzmann) statistics known as quons is discussed. The picture of Bose/Fermi particles as low energy excitations over nontrivial quon condensate is advocated. Using induced gravity arguments it is demonstrated that the Planck mass in such low energy effective theory can be factorially (in number of degrees of freedom) larger than its true ultraviolet cutoff. Thus, the assumption that statistics of relevant high energy excitations is neither Bose nor Fermi but infinite can remove the hierarchy problem without necessity to introduce any artificially large numbers. Quantum mechanical model illustrating this scenario is presented.