Vacuum structure and string tension in Yang-Mills dimeron ensembles

TL;DR

This study uses numerical simulations of SU(2) Yang-Mills dimeron ensembles to explore their topological and confinement properties, demonstrating that dissociating dimerons into merons can produce a confining phase consistent with known phenomenology.

Contribution

It provides the first comprehensive numerical evidence that dimeron dissociation into merons can generate confinement in Yang-Mills theory without relying on weak-coupling approximations.

Findings

Dimeron ensembles exhibit short-range order at small coupling that screens topological charges.

Increasing coupling causes dimerons to dissociate into merons, leading to a finite, increasing string tension.

Results match standard values for action density and topological susceptibility in the physical coupling region.

Abstract

We numerically simulate ensembles of SU(2) Yang-Mills dimeron solutions with a statistical weight determined by the classical action and perform a comprehensive analysis of their properties. In particular, we examine the extent to which these ensembles capture topological and confinement properties of the Yang-Mills vacuum. This further allows us to test the classic picture of meron-induced quark confinement as triggered by dimeron dissociation. At small bare couplings, spacial, topological-charge and color correlations among the dimerons generate a short-range order which screens topological charges. With increasing coupling this order weakens rapidly, however, in part because the dimerons gradually dissociate into their meron constituents. Monitoring confinement properties by evaluating Wilson-loop expectation values, we find the growing disorder due to these progressively liberated merons to generate a finite and (with the coupling) increasing string tension. The short-distance behavior of the static quark-antiquark potential, on the other hand, is dominated by small, "instanton-like" dimerons. String tension, action density and topological susceptibility of the dimeron ensembles in the physical coupling region turn out to be of the order of standard values. Hence the above results demonstrate without reliance on weak-coupling or low-density approximations that the dissociating dimeron component in the Yang-Mills vacuum can indeed produce a meron-populated confining phase. The density of coexisting, hardly dissociated and thus instanton-like dimerons seems to remain large enough, on the other hand, to reproduce much of the additional phenomenology successfully accounted for by non-confining instanton vacuum models. Hence dimeron ensembles should provide an efficient basis for a rather complete description of the Yang-Mills vacuum.