This review discusses confinement, as well as the topological and critical phenomena, in the gauge theories which provide the condensation of magnetic monopoles. These theories include the 3D SU(N
) Georgi-Glashow model, the 4D [U(1)]
-invariant compact QED , and the [U(1)]
-invariant dual Abelian Higgs model. After a general introduction to the string models of confinement, an analytic description of this penomenon is provided at the example of the 3D SU(N
) Georgi-Glashow model, with a special emphasis placed on the so-called Casimir scaling of k
-string tensions in that model. We further discuss the string representation of the 3D [U(1)]
-invariant compact QED, as well as of its 4D generalization with the inclusion of the
-term. We compare topological effects, which appear in the latter case, with those that take place in the 3D QED extended by the Chern-Simons term. We further discuss the string representation of the ’t Hooft-loop average in the [U(1)]
-invariant dual Abelian Higgs model extended by the
-term, along with the topological effects caused by this term. These topological effects are compared with those occurring in the 3D dual Abelian Higgs model (i.e., the dual Landau-Ginzburg theory) extended by the Chern-Simons term. In the second part of the review, we discuss critical properties of the weakly-coupled 3D confining theories. These theories include the 3D compact QED, along with its fermionic extension, and the 3D Georgi-Glashow model.
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