Evidence for fine tuning of fermionic modes in lattice gluodynamics
F. V. Gubarev*, S. M. Morozov*, M. I. Polikarpov*, V. I. Zakharov+
+Institute of Theoretical and Experimental Physics, 117259 Moscow, Russia
*Max-Planck Institut für Physik, 80805 München, Germany
PACS: 11.15.Ha, 11.30.Rd, 12.38.Gc
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 cut off. 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.