Quantum weights of dyons and of instantons with nontrivial holonomy

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, ΛQCD, 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 ΛQCD, trivial holonomy is unstable, and that calorons "ionize" into separate dyons.

Instantons at work

“…(2.54) the potential first rises as function of the interquark separation but asymptotically it flattens out. If the size distribution happens to fall off as d(ρ) ∼ 1/ρ 3 at large ρ one gets a linear infinitely rising potential [38]. However, such a size distribution means that large instantons inevitably overlap, which means that the "center, size, orientations" collective cooredinates are not the most adequate.…”

“…Instantons induce certain potential between static quarks in the pure glue theory, which depends on the instanton size distribution [4,14,38]. For fast convergent size distributions like that given by eq.…”

Improved superposition schemes for approximate multi-caloron configurations

“…All these lattice studies had been and are performed, in order to empirically fix the instanton or caloron content of the simulated fields. The necessity of considering now caloron-anticaloron gases is reflected by the fact that a strictly semiclassical calculation, which has been done for a single caloron [19], is not feasible from the bottom up in a strongly coupled system like QCD. Ideas about caloron constituents as relevant degrees of freedom for the confined phase from the point of view of electric-magnetic duality have been developed in Ref.…”

Calorons and dyons at the thermal phase transition analyzed by overlap fermions

“…It has been guessed that calorons with intermediate holonomy 3 would describe the topological structure in the high-T phase closely above T dec . A semiclassical evaluation of the path integral [60] has shown, however, that the caloron becomes unstable against dissociation into dyons outside a narrow stability region |L| > 0.72. On the lattice, by suitable measures of selfduality [47,61], it has been observed that locally selfdual domains become suppressed above T dec .…”