Instanton size distribution: repulsion or the infrared fixed point?

Abstract

We discuss available information about the instanton size distribution $d(ρ)$, which comes from lattice simulations and the interacting instanton liquid model. Not only they are remarkably consistent, but one can also reproduce $d(ρ)$ 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 $8π^2/g^2= N_c*5.4$ when it is the case.