Quantum weights of dyons and of instantons with non-trivial holonomy

TL;DR

This paper computes the quantum weights of calorons with non-trivial holonomy in Yang-Mills theory, revealing their dependence on holonomy, temperature, and monopole separation, and showing that trivial holonomy becomes unstable at low temperatures.

Contribution

It provides an exact calculation of functional determinants for periodic instantons with non-trivial holonomy, elucidating their weights and stability properties in the Yang-Mills partition function.

Findings

Quantum weights depend on holonomy, temperature, and monopole separation.

At large dyon separation, the measure factorizes into individual dyon measures.

Below a critical temperature, trivial holonomy is unstable and calorons dissociate into dyons.

Abstract

We calculate exactly functional determinants for quantum oscillations about periodic instantons with non-trivial value of the Polyakov line at spatial infinity. Hence, we find the weight or the probability with which calorons with non-trivial holonomy occur in the Yang--Mills partition function. The weight depends on the value of the holonomy, the temperature, Lambda_QCD, and the separation between the BPS monopoles (or dyons) which constitute the periodic instanton. At large separation between constituent dyons, the quantum measure factorizes into a product of individual dyon measures, times a definite interaction energy. We present an argument that at temperatures below a critical one related to Lambda_QCD, trivial holonomy is unstable, and that calorons ``ionize'' into separate dyons.