Quantum weights of dyons and of instantons with nontrivial holonomy

Abstract

We calculate exactly functional determinants for quantum oscillations about periodic instantons with a nontrivial value of the Polyakov line at spatial infinity. Hence, we find the weight or the probability with which calorons with nontrivial holonomy occur in the Yang-Mills partition function. The weight depends on the value of the holonomy, the temperature, ${\ensuremath{\Lambda}}_{\mathrm{QCD}},$ and the separation between the BPS monopoles (or dyons) that 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 ${\ensuremath{\Lambda}}_{\mathrm{QCD}},$ trivial holonomy is unstable, and that calorons ``ionize'' into separate dyons.