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Superconductivity in supersymmetric theories. (English) Zbl 1252.81102

Summary: A study of superconductivity is undertaken through the breaking of supersymmetric gauge theories which automatically incorporate the condensation of monopoles and dyons leading to confining and superconducting phases. Constructing the effective Lagrangian near a singularity in the moduli space for the \(N=2\) supersymmetric theory with \(SU(2)\) gauge group, it is shown that, when a mass term is added to this Lagrangian, the \(N=2\) supersymmetry is reduced to the \(N=1\) supersymmetry yielding dyonic condensation which leads to confinement and superconductivity as a consequence of the generalized Meissner effect. In the Coulomb phase of the \(N=2 SU(3)\) Yang-Mills theory, the gauge symmetry is broken down to \(SU(2)\times U(l)\), and it is shown that, when it is perturbed by a suitable tree-level superpotential, this supersymmetry theory breaks to the \(N=1 SU(2)\) Yang-Mills theory described by the Higgs field in confining phase incorporating superconductivity.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
82D55 Statistical mechanics of superconductors
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