Abstract
We propose a gauge-independent mechanism for the area-law behavior of Wilson loop expectation values in terms of worldsheets spanning Wilson loops interacting with the spin foams that contribute to the vacuum partition function. The method uses an exact transformation of lattice-regularized Yang–Mills theory that is valid for all couplings. Within this framework, some natural conjectures can be made as to what physical mechanism enforces the confinement property in the continuum (weak coupling) limit. Details for the SU ( 2 ) case in three space–time dimensions are provided in a companion paper.
Highlights
Our current understanding of confinement in Yang-Mills gauge theories encompasses a seemingly diverse collection of approaches, including center vortices [37], dual superconductors [28, 33, 38], and effective strings of various types [5, 32] — to name just a few that have attracted interest over the years.In the present work we propose a mechanism for confinement that is similar in concept to the well-known proof of confinement in the strong coupling limit [30], but suitably generalized so that the analysis is valid at the arbitrarily weak couplings that are characteristic of the continuum limit
Based on some elementary considerations that allow Wilson loop expectation values to be expressed as a double sum over worldsheets and vacuum spin foam backgrounds, we have attempted to map out some of the properties we expect to hold at weak coupling in order to provide an area-law decay
The concepts introduced in this paper can summarized as follows: (1) Wilson loop expectation values can be expressed as a certain type of observable having the form of a sum over worldsheets bounded by Γ
Summary
Our current understanding of confinement in Yang-Mills gauge theories encompasses a seemingly diverse collection of approaches, including center vortices [37], dual superconductors [28, 33, 38], and effective strings of various types [5, 32] — to name just a few that have attracted interest over the years. In the present work we propose a mechanism for confinement that is similar in concept to the well-known proof of confinement in the (unphysical) strong coupling limit [30], but suitably generalized so that the analysis is valid at the arbitrarily weak couplings that are characteristic of the continuum limit. This will allow us to give a brief account of the widely known proof of confinement at strong coupling and fix basic notation to be used throughout.
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