If one gauge theory has a confined phase, does this theory also have a scale? (eg. QCD has the confined phase and it also has the QCD scale)
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1$\begingroup$ If there is a transition, there is a natural scale in the problem. In condensed matter, this would be the critial temperature. $\endgroup$– TabinCommented Nov 12 at 23:51
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$\begingroup$ Detail what you understand about the "confinement phase", and answers might emerge to help you... $\endgroup$– Cosmas ZachosCommented Nov 13 at 0:59
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$\begingroup$ Linked. $\endgroup$– Cosmas ZachosCommented Nov 13 at 1:11
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$\begingroup$ A million dollar question, according to Clay, albeit up to interpretation. $\endgroup$– MadMaxCommented Nov 13 at 16:33
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1 Answer
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Here are various statements that may or may not be helpful for you:
- If you actually had a phase transition in a gauge theory at some temperature $T_c$ between two different phases of matter, (confined and deconfined), of course $T_c$ provides a natural scale for the theory.
- QCD itself (with physical values for all the quark masses) doesn't have a phase transition at zero chemical potential, it is actually a crossover. You can still define effective crossover temperatures if you like. If you vary the masses of the quarks, you can also change the behaviour from a crossover to a genuine phase transition (this is the content of the `Columbia Plot').
- What people usually mean by the `QCD scale' is $\Lambda_\mathrm{QCD}$, which isn't usually defined in terms of the deconfinement transition, but rather by analysis of the perturbative running of the strong coupling constant.
