The emergence of superconducting systems in Anti-de Sitter space

Abstract

In this article, we investigate the mathematical relationship between a (3+1) dimensional gravity model inside Anti-de Sitter space AdS 4 , and a (2+1) dimensional superconducting system on the asymptotically flat boundary of AdS 4 (in the absence of gravity). We consider a simple case of the Type II superconducting model (in terms of Ginzburg-Landau theory) with an external perpendicular magnetic field H. An interaction potential V (r, ψ) = α(T )|ψ| 2 /r 2 + χ|ψ| 2 /L 2 + β|ψ| 4 /(2r k ) is introduced within the Lagrangian system. This provides more flexibility within the model, when the superconducting system is close to the transition temperature T c . Overall, our result demonstrates that the Ginzburg-Landau differential equations can be directly deduced from Einstein's theory of general relativity.