Abstract
The mechanism of confinement in Yang-Mills theories remains a challenge to our understanding of nonperturbative gauge dynamics. While it is widely perceived that confinement may arise from chromo-magnetically charged gauge configurations with nontrivial topology, it is not clear what types of configurations could do that and how, in pure Yang-Mills and QCD-like (non-supersymmetric) theories. Recently a promising approach has emerged, based on statistical ensembles of dyons/anti-dyons that are constituents of instanton/anti-instanton solutions with nontrivial holonomy where the holonomy plays a vital role as an effective "Higgsing" mechanism. We report a thorough numerical investigation of the confinement dynamics in SU(2) Yang-Mills theory by constructing such a statistical ensemble of correlated instanton-dyons.
Highlights
The quantum chromodynamics, or QCD, is established as the fundamental quantum field theory of strong nuclear force underlying all of nuclear physics
We report a thorough numerical investigation of the confinement dynamics in SUð2Þ Yang-Mills theory by constructing such a statistical ensemble of correlated instanton-dyons
Our main conclusion is that such an ensemble correctly produces the various essential features of the confinement dynamics from above to below the transition temperature
Summary
The quantum chromodynamics, or QCD, is established as the fundamental quantum field theory of strong nuclear force underlying all of nuclear physics. A crucial difference of pure Yang-Mills or QCD (as compared with, e.g., GeorgeGlashow model or Seiberg-Witten therory) is that they do not have adjoint scalar fields which would provide the natural “Higgsing” on the spatial boundary, allowing the construction of magnetic monopole solutions. The nontrivial holonomy provides the needed nontrivial boundary constraints (which would have to come from the adjoint scalar fields in “Higgsed” theories) Owing to such important new features, the KvBLL calorons with their dyon constituents provide the unique topological configurations that could potentially account for the nonperturbative dynamics underlying confinement. In addition a few Appendices are included to explain some “background” information in detail and to make the paper more self-contained for the convenience of readers
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