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.

arXiv commentPrepared 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

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Cited by in corpus (8)

• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Confinement from semiclassical gluon fields in SU(2) gauge theory
• Fermi-Einstein condensation in dense QCD-like theories
• On the Continuum Limit of Topological Charge Density Distribution
• Effective scalar fields in Yang-Mills theories
• Shrinking fermionic modes, on the lattice and in the continuum
• Flux-Tube Formation and Holographic Tunneling
• Nonperturbative physics at short distances