An Analytic Holographic Superconductor

Abstract

We investigate a holographic superconductor that admits an analytic treatment near the phase transition. In the dual 3+1 dimensional field theory, the phase transition occurs when a scalar operator of scaling dimension two gets a vacuum expectation value. We calculate current-current correlation functions along with the speed of second sound near the critical temperature. We also make some remarks about critical exponents. An analytic treatment is possible because an underlying Heun equation describing the zero mode of the phase transition has a polynomial solution. Amusingly, the treatment here may generalize for an order parameter with any integer spin, and we propose a Lagrangian for a spin two holographic superconductor.

20 pages; v2 ref, comment about non-mean field exponents added; v3 several typos fixed

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• Surprising Connections Between General Relativity and Condensed Matter
• Maxwell-Chern-Simons Vortices and Holographic Superconductors
• d-wave Holographic Superconductor Vortex Lattice and Non-Abelian Holographic Superconductor Droplet
• Refractive index in holographic superconductors
• Characteristic length of a Holographic Superconductor with $d$-wave gap
• Critical phenomena in the AdS/CFT duality
• Analytical approach to phase transitions in rotating and non-rotating 2D holographic superconductors
• Particle-hole instability in the $Ad{S}_4$ holography
• Notes on relativistic superfluidity and gauge/string duality