On Statistical Mechanics of Instantons in the CP^{N_c-1} Model

TL;DR

This paper develops an explicit multi-instanton weight for the CP^{N_c-1} model, analyzing the statistical mechanics of instantons and anti-instantons using both analytical and numerical methods, revealing that most topological charge resides in well-separated instantons.

Contribution

It introduces a new parametrization of multi-instantons via 'zindons' and studies their statistical mechanics, including interactions, in the CP^{N_c-1} model.

Findings

Most topological charge is in well-separated instantons and anti-instantons.

The zindon parametrization enables complete instanton 'melting'.

Analytical and numerical methods agree on the dominance of separated instantons.

Abstract

We introduce an explicit form of the multi-instanton weight including also instanton--anti-instanton interactions for arbitrary $N_c$ in the two-dimensional $CP^{N_c-1}$ model. To that end, we use the parametrization of multi-instantons in terms of instanton `constituents' which we call `zindons' for short. We study the statistical mechanics of zindons analytically (by means of the Debye-H\"uckel approximation) and numerically (running a Metropolis algorithm). Though the zindon parametrization allows for a complete `melting' of instantons we find that, through a combination of dynamical and purely geometric factors, a dominant portion of topological charge is residing in well-separated instantons and anti-instantons.