Evidence for fine tuning of fermionic modes in lattice gluodynamics

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, they 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 briefly discuss the possible theoretical implications and also include some general, review-type remarks.