Evidence for fine tuning of fermionic modes in lattice gluodynamics

TL;DR

This paper investigates the properties of fermionic modes in lattice gluodynamics, revealing their sensitivity to both physical and ultraviolet scales, and suggesting they are finely tuned in the quantum vacuum.

Contribution

It provides evidence that fermionic zero and near-zero modes are finely tuned, sensitive to both physical and ultraviolet scales, which is a novel insight into lattice gluodynamics.

Findings

Fermionic modes are sensitive to the underlying gluonic topology.

The density of states is in physical units.

Localization volume of modes tends to zero as lattice spacing decreases.

Abstract

We consider properties of zero and near-zero fermionic modes in lattice gluodynamics. The modes are known to be sensitive to the topology of the underlying gluonic fields in the quantum vacuum state of the gluodynamics. We find evidence that these modes are fine tuned, that is exhibit sensitivity to both physical (one can say, hadronic) scale and to the ultraviolet cutoff. Namely, the density of the states is in physical units while the localization volume of the modes tends to zero in physical units with the lattice spacing tending to zero. We discuss briefly possible theoretical implications and also include some general, review-type remarks.