Dynamical suppression of large instantons

TL;DR

This paper models instanton size distributions considering non-diluteness, showing large instantons are suppressed dynamically, with results aligning with semi-classical and lattice findings.

Contribution

It introduces a simplified model incorporating instanton interactions via a repulsive core, providing a self-consistent approach to suppress large instantons.

Findings

Small instanton sizes follow a power law distribution.

Large instanton sizes decay exponentially.

Model results agree with lattice simulation data.

Abstract

We investigate the distribution of instanton sizes in the framework of a simplified model for ensembles of instantons. This model takes into account the non-diluteness of instantons. The infrared problem for the integration over instanton sizes is dealt with in a self-consistent manner by approximating instanton interactions by a repulsive hard core potential. This leads to a dynamical suppression of large instantons. The characteristic features of the instanton size distribution are studied by means of analytic and Monte Carlo methods. We find a power law behaviour for small sizes, consistent with the semi-classical results. At large instanton sizes the distribution decays exponentially. The results are compared with those from lattice simulations.