We show that a simple gravitational theory can provide a holographically dual description of a superconductor. There is a critical temperature, below which a charged condensate forms via a second order phase transition and the (dc) conductivity becomes infinite. The frequency dependent conductivity develops a gap determined by the condensate. We find evidence that the condensate consists of pairs of quasiparticles.

The discussion of holographic techniques progresses from equilibrium, to transport and to superconductivity.arXiv:0903.3246v2 [hep-th]

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We present a general hydrodynamic theory of transport in the vicinity of superfluid-insulator transitions in two spatial dimensions described by "Lorentz"-invariant quantum critical points. We allow for a weak impurity scattering rate, a magnetic field B, and a deviation in the density from that of the insulator. We show that the frequency-dependent thermal and electric linear response functions, including the Nernst coefficient, are fully determined by a single transport coefficient ͑a universal electrical conductivity͒, the impurity scattering rate, and a few thermodynamic state variables. With reasonable estimates for the parameters, our results predict a magnetic field and temperature dependence of the Nernst signal which resembles measurements in the cuprates, including the overall magnitude. Our theory predicts a "hydrodynamic cyclotron mode" which could be observable in ultrapure samples. We also present exact results for the zero frequency transport coefficients of a supersymmetric conformal field theory ͑CFT͒, which is solvable by the anti-de Sitter ͑AdS͒/CFT correspondence. This correspondence maps the and B perturbations of the 2 + 1 dimensional CFT to electric and magnetic charges of a black hole in the 3 + 1 dimensional anti-de Sitter space. These exact results are found to be in full agreement with the general predictions of our hydrodynamic analysis in the appropriate limiting regime. The mapping of the hydrodynamic and AdS/CFT results under particle-vortex duality is also described.

Abstract:We initiate a holographic model building approach to 'strange metallic' phenomenology. Our model couples a neutral Lifshitz-invariant quantum critical theory, dual to a bulk gravitational background, to a finite density of gapped probe charge carriers, dually described by D-branes. In the physical regime of temperature much lower than the charge density and gap, we exhibit anomalous scalings of the temperature and frequency dependent conductivity. Choosing the dynamical critical exponent z appropriately we can match the non-Fermi liquid scalings, such as linear resistivity, observed in strange metal regimes. As part of our investigation we outline three distinct string theory realizations of Lifshitz geometries: from F theory, from polarised branes, and from a gravitating charged Fermi gas. We also identify general features of renormalisation group flow in Lifshitz theories, such as the appearance of relevant charge-charge interactions when z ≥ 2. We outline a program to extend this model building approach to other anomalous observables of interest such as the Hall conductivity.