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.

Prepared for Miniconference `Sense of Beauty in Physics' in honor of Adriano Di Giacomo on occasion of his 70th Birthday, Pisa, Italy, 26-27 Jan 2006

References in corpus (3)

• On the Continuum Limit of Topological Charge Density Distribution
• Fine Tuning in Lattice SU(2) Gluodynamics vs Continuum-Theory Constraints
• Topologically non-trivial field configurations - interplay of vortices and Dirac eigenmodes

Cited by in corpus (6)

• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• On the Continuum Limit of Topological Charge Density Distribution
• Flux-Tube Formation and Holographic Tunneling
• Shrinking fermionic modes, on the lattice and in the continuum
• Effective scalar fields in Yang-Mills theories
• Nonperturbative physics at short distances