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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?

Dough
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1 Answers1

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

http://adsabs.harvard.edu/abs/1979NuPhB.160..349B

and Fradkin Shenker 1979:

http://prd.aps.org/abstract/PRD/v19/i12/p3682_1

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:

http://arxiv.org/abs/hep-th/9408155

In some cases, the confinement and Higgs phases may be distinct. The relationships between the two phenomena may be understood as a sort of S-duality - a strong-weak duality or a generalized electro-magnetic duality. For example, the last paper I quoted explains why confinement may be understood as condensation of monopoles (the dual, "magnetically" charged particles, which is kind of the S-dual of the normal Higgs mechanism which gives vevs to "electrically" charged fields).

Supersymmetric gauge theories are full of S-dualities, much like stringy vacua.

Luboš Motl
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