Quantum weights of monopoles and calorons with non-trivial holonomy

Abstract

The functional determinant is computed exactly for quantum oscillations about periodic instantons with non-trivial values of the Polyakov line at spatial infinity (or holonomy). Such instantons can be viewed as composed of the Bogomolnyi--Prasad--Sommerfeld (BPS) monopoles or dyons. We find the weight or the probability with which dyons occur in the pure Yang--Mills partition function. It turns out that dyons experience quantum interactions having the familiar "linear plus Coulomb" form but with the "string tension'' depending on the holonomy. We present an argument that at temperatures below the critical one computed from Lambda_QCD, trivial holonomy becomes unstable, with instantons ``ionizing'' into separate dyons. It may serve as a microscopic mechanism of the confinement-deconfinement phase transition.