Instanton size distribution: repulsion or the infrared fixed point?

Abstract

We discuss available information about the instanton size distribution $d(\rho )$, which comes from lattice simulations and the interacting instanton liquid model. Not only they are remarkably consistent, but one can also reproduce $d(\rho )$ with an alternative idea, based on the infrared fixed point. We show, that lattice non-perturbative beta-function (for $bare$ charge renormalization) also suggests such a hint. We also discuss whether it is possible to reconcile the instanton physics with reasonable large-number-of-colors limit, concluding that our fits for SU(2) and SU(3) theories are actually very close to the critical value $8{\pi }^2/g^2=N_c\ast 5.4$ when it is the case.

Comments: Figures as .ps file