Spherically Symmetric Chromostatic Condensates as an Introduction to the Strong Conjecture for Color Confinement

TL;DR

This paper explores spherically symmetric chromostatic condensates in non-Abelian gauge theories, proposing a solitonic model that supports the strong conjecture of color confinement via topological domain walls.

Contribution

It introduces a novel solitonic description of color confinement using spherically symmetric solutions to Yang-Mills equations, linking interior and exterior hadronic volumes.

Findings

Chromostatic condensates can be described by solitonic solutions.

Topological domain walls separate hadron interior from vacuum.

Model aligns with the strong conjecture for color confinement.

Abstract

Nonlinearities imbedded in the Lagrange density for non-Abelian gauge theories produce solutions to the Yang-Mills Maxwell equations that describe spatially extended chromostatic condensates. For solutions in spherically-symmetric SU(2) the topological structures separating such condensates provide a specific solitonic description of color confinement. The strong Conjecture The confinement mechanism for QCD involves a domain wall of topological (CP-odd) charge separating the interior volume of hadrons from an exterior volume. To explain the consequences of this conjecture we describe spherically symmetric chromostatic condensates that are consistent with the interior volume of a hadron and other condensates that are consistent with exterior vacuum volume. We then demonstrate how the Yang-Mills Maxwell equations can connect the two volumes with a soliton domain wall. The preliminary phenomenological description described here does not deal explicitly either with charged fermions or with the quantization of non-Abelian dynamics.