TL;DR
This paper links the knot equation in Skyrme theory to the SU(2) QCD vacuum potential, revealing three equivalent descriptions of the QCD vacuum and its topological classification via an Abelian gauge potential.
Contribution
It demonstrates that the QCD vacuum can be characterized by an Abelian gauge potential with a Chern-Simons index, connecting knot theory and QCD vacuum structure.
Findings
QCD vacuum can be described by a non-linear sigma field, a complex vector field, or an Abelian gauge potential.
The knot equation of Skyrme theory relates to the vacuum potential of SU(2) QCD.
QCD vacuum classification is possible through an Abelian gauge potential with topological index.
Abstract
We show that one can express the knot equation of Skyrme theory completely in terms of the vacuum potential of SU(2) QCD, in such a way that the equation is viewed as a generalized Lorentz gauge condition which selects one vacuum for each class of topologically equivalent vacua. From this we show that there are three ways to describe the QCD vacuum (and thus the knot), by a non-linear sigma field, a complex vector field, or by an Abelian gauge potential. This tells that the QCD vacuum can be classified by an Abelian gauge potential with an Abelian Chern-Simon index.
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