# Why are the Higgs phase and the confinement phase identical in Yang-Mills-Higgs systems?

If we couple a Yang-Mills theory with a Higgs field and some quarks in the fundamental representation, we can have a Higgs phase and a confining phase. However, they are indistinguishable. The Wilson loops scale according to the perimeter law, not the area law in the confining phase because of hadronization. In the Higgs phase, there is no cluster decomposition for the Higgs field because distant points have to be connected by a Wilson line with exponential falloff as the length of the Wilson line.

Why are both phases indistinguishable?

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I'm not really sure what you mean by "because of hadronization"; there are confining theories that are truly confining (have an area law), like pure Yang-Mills, where the spectrum is still a set of hadrons (glueballs, in that case). The reason this isn't true when quarks are in the fundamental representation is that strings can break, so asymptotically there isn't a linearly rising potential between static quarks. –  Matt Reece Feb 24 '11 at 15:34

Dough, in some cases, the Higgs and confinement phases are not separated at all and form the total screening phase, see Banks Rabinovici 1979:

More recently, those and similar relationships were studied in the context of supersymmetric field theories and supersymmetric string vacua. The papers by Seiberg and Witten for $N=2$ were the main progress. See also papers such as this random one: