The emergence of superconducting systems in Anti-de Sitter space

W. M. Wu, M. P. Pierpoint, D. M. Forrester, F. V. Kusmartsev

Research output: Contribution to journalArticlepeer-review


In this article, we investigate the mathematical relationship between a (3+1) dimensional gravity model inside Anti-de Sitter space AdS4, and a (2+1) dimensional superconducting system on the asymptotically flat boundary of AdS4 (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/r2 + χ|ψ|2/L2 + β|ψ|4/(2rk) is introduced within the Lagrangian system. This provides more flexibility within the model, when the superconducting system is close to the transition temperature Tc. Overall, our result demonstrates that the Ginzburg-Landau differential equations can be directly deduced from Einstein’s theory of general relativity.

Original languageBritish English
Article number17
JournalJournal of High Energy Physics
Issue number10
StatePublished - 1 Oct 2016


  • Classical Theories of Gravity
  • Duality in Gauge Field Theories
  • Holography and condensed matter physics (AdS/CMT)


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