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A holographic superconductor in an external magnetic field. (English) Zbl 1245.81075

Summary: We study a system of a complex charged scalar coupled to a Reissner-Nordström black hole in \(3+1\) dimensional anti-de Sitter spacetime, neglecting back-reaction. With suitable boundary conditions, the cases of a neutral and purely electric black hole have been studied in various limits and were shown to yield key elements of superconductivity in the dual \(2+1\) dimensional field theory, forming a condensate below a critical temperature. By adding magnetic charge to the black hole, we immerse the superconductor into an external magnetic field. We show that a family of condensates can form and we examine their structure. For finite magnetic field, they are localized in one dimension with a profile that is exactly solvable, since it maps to the quantum harmonic oscillator. As the magnetic field increases, the condensate shrinks in size, which is reminiscent of the Meissner effect.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
82D55 Statistical mechanics of superconductors
81T20 Quantum field theory on curved space or space-time backgrounds