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Analytical holographic superconductor with backreaction using \(AdS_3/CFT_2\). (English) Zbl 1274.83086
Summary: The holographic model for a two-dimensional superconductor has been investigated by considering the three-dimensional gravity in the bulk. To find the critical temperature, we used the Sturm-Liouville variational method. Where as the same method is applied for calculating the condensation of the dual operators on the boundary. We included the back reactions on the metric by a combination of the perturbation method of the fields with respect to the small parameter and then applying the variational integrals on the resulting equations of the motion. The critical temperature has been successfully obtained on the backreaction effects, and we showed that it dropped with a rise in the backreaction of the fields, and it makes the condensation harder. We can use our analytical results to support the numerical data which was reported previously.

MSC:
83C57 Black holes
83E30 String and superstring theories in gravitational theory
82D55 Statistical mechanical studies of superconductors
81T05 Axiomatic quantum field theory; operator algebras
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