Distribution of instanton sizes in a simplified instanton gas model

TL;DR

This paper studies the distribution of instanton sizes in a simplified model that accounts for instanton interactions, revealing a power law at small sizes and exponential decay at large sizes, with results supported by analytic, Monte Carlo, and lattice methods.

Contribution

It introduces a self-consistent approach to modeling instanton size distribution considering non-diluteness and interaction effects, providing new analytic and numerical insights.

Findings

Power law behavior for small instantons

Exponential decay for large instantons

Agreement with lattice simulation results

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. In one dimension exact results can be derived. In any dimension 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.