Holographic P-wave Superconductors in 1+1 Dimensions

Abstract

We study $(1+1)$-dimensional p-wave holographic superconductors described by three dimensional Einstein-Maxwell gravity coupled to a massive complex vector field in the context of $Ad{S}_3/CF{T}_2$ correspondence. In the probe limit where the backreation of matter fields is neglected, we show that there occurs a formation of a vector hair around the black hole below a certain critical temperature. In the dual strongly coupled $(1+1)$-dimensional boundary theory, this holographically corresponds to the formation of a charged vector condensate spontaneously breaking both the $U(1)$ and $SO(1,1)$ symmetries. We numerically compute the ac conductivity for the superconducting phase of the boundary field theory and find that the presence of a magnetic moment term in the dual bulk theory effects the conductivity in the boundary field theory.

21 pages and 8 figures, one section on free energy computation is added

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• Conductivity of the one-dimensional holographic p-wave superconductors in the presence of nonlinear electrodynamics
• Transport properties of a $3$-dimensional holographic effective theory with gauge-axion coupling
• Holographic Superconductors: An Analytic Method Revisit
• Topological Field Theory and Stochastic Dynamics