In the context of Yang Mills Theory, what is quark confinement? Please try to explain as simple as possible (obviously without being too general)
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$\begingroup$ Veritasium has some videos on it. youtube.com/watch?v=Ztc6QPNUqls, youtube.com/watch?v=J3xLuZNKhlY $\endgroup$– mmesser314Commented Feb 8, 2020 at 3:51
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$\begingroup$ The concept of a pure Yang Mills Theory is one where we (usually?) only have the gauge fields and no fermions. But you are asking about quark confinement. Do you have in mind a non-abelian gauge theory with fermions? $\endgroup$– flippiefanusCommented Feb 8, 2020 at 4:08
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$\begingroup$ Gluon-gluon interactions cause the gluon field between a quark and an antiquark to be concentrated in a flux tube that acts like a string between them. Instead of the potential energy going like $1/r$ between them, it goes like $r$. $\endgroup$– G. SmithCommented Feb 8, 2020 at 5:35
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1$\begingroup$ Did you read the Wikipedia page? $\endgroup$– Qmechanic ♦Commented Feb 8, 2020 at 8:45
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1 Answer
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As Wikipedia explains,
The phenomenon can be understood qualitatively by noting that the force-carrying gluons of QCD have color charge, unlike the photons of quantum electrodynamics (QED). Whereas the electric field between electrically charged particles decreases rapidly as those particles are separated, the gluon field between a pair of color charges forms a narrow flux tube (or string) between them. Because of this behavior of the gluon field, the strong force between the particles is constant regardless of their separation.
Therefore, as two color charges are separated, at some point it becomes energetically favorable for a new quark–antiquark pair to appear, rather than extending the tube further. As a result of this, when quarks are produced in particle accelerators, instead of seeing the individual quarks in detectors, scientists see "jets" of many color-neutral particles (mesons and baryons), clustered together. This process is called hadronization, fragmentation, or string breaking.
Mathematically, confinement is related to QCD having a nonabelian gauge group, $SU(3)$. This leads to the gluon field interacting with itself in a nonlinear way, which, for $SU(3)$ gauge theory in $3+1$ dimensions, then leads to color confinement.
