Matter of resolution: from quasiclassics to fine tuning

Abstract

Recently, there appeared results of lattice measurements in Yang-Mills theories which indicate non-trivial dependences on the lattice spacing of many observables. In particular, volume occupied by fermionic zero modes shrinks to zero in the continuum limit. These results are in apparent disagreement with quasiclassical models which assume that all the non-perturbative effects develop on the scale of $\Lambda_{QCD}$. We emphasize that this kind of contradictions might be superficial since the results in point depend in fact on the measurements procedure. The lattice simulations correspond to measurements with high resolution while the quasiclassical picture assumes poor resolution. We will argue that the general trend is that what looks quasiclassical in measurements with poor resolution becomes fine tuned in measurements with fine resolution. The main emphasis is on the topological fermionic modes and we argue that shrinking of the volume occupied by the modes could have been predicted theoretically.