Cooper pairing near charged black holes

We show that a quartic contact interaction between charged fermions can lead to Cooper pairing and a superconducting instability in the background of a charged asymptotically Anti-de Sitter black hole. For a massless fermion we obtain the zero mode analytically and compute the dependence of the critical temperature T_c on the charge of the fermion. The instability we find occurs at charges above a critical value, where the fermion dispersion relation near the Fermi surface is linear. The critical temperature goes to zero as the marginal Fermi liquid is approached, together with the density of states at the Fermi surface. Besides the charge, the critical temperature is controlled by a four point function of a fermionic operator in the dual strongly coupled field theory.Comment: 1+33 pages, 4 figure

Holographic metals at finite temperature

A holographic dual description of a 2+1 dimensional system of strongly interacting fermions at low temperature and finite charge density is given in terms of an electron cloud suspended over the horizon of a charged black hole in asymptotically AdS spacetime. The electron star of Hartnoll and Tavanfar is recovered in the limit of zero temperature, while at higher temperatures the fraction of charge carried by the electron cloud is reduced and at a critical temperature there is a second order phase transition to a configuration with only a charged black hole. The geometric structure implies that finite temperature transport coefficients, including the AC electrical conductivity, only receive contributions from bulk fermions within a finite band in the radial direction.Comment: LaTex 16 pages, 12 figures, v2: Added reference. Error in free energy corrected. Phase transition to AdS-RN black brane is third order rather than second order as was claimed previousl

Shear Modes, Criticality and Extremal Black Holes

We consider a (2+1)-dimensional field theory, assumed to be holographically dual to the extremal Reissner-Nordstrom AdS(4) black hole background, and calculate the retarded correlators of charge (vector) current and energy-momentum (tensor) operators at finite momentum and frequency. We show that, similar to what was observed previously for the correlators of scalar and spinor operators, these correlators exhibit emergent scaling behavior at low frequency. We numerically compute the electromagnetic and gravitational quasinormal frequencies (in the shear channel) of the extremal Reissner-Nordstrom AdS(4) black hole corresponding to the spectrum of poles in the retarded correlators. The picture that emerges is quite simple: there is a branch cut along the negative imaginary frequency axis, and a series of isolated poles corresponding to damped excitations. All of these poles are always in the lower half complex frequency plane, indicating stability. We show that this analytic structure can be understood as the proper limit of finite temperature results as T is taken to zero holding the chemical potential fixed.Comment: 28 pages, 7 figures, added reference

Universal thermal and electrical conductivity from holography

It is known from earlier work of Iqbal, Liu (arXiv:0809.3808) that the boundary transport coefficients such as electrical conductivity (at vanishing chemical potential), shear viscosity etc. at low frequency and finite temperature can be expressed in terms of geometrical quantities evaluated at the horizon. In the case of electrical conductivity, at zero chemical potential gauge field fluctuation and metric fluctuation decouples, resulting in a trivial flow from horizon to boundary. In the presence of chemical potential, the story becomes complicated due to the fact that gauge field and metric fluctuation can no longer be decoupled. This results in a nontrivial flow from horizon to boundary. Though horizon conductivity can be expressed in terms of geometrical quantities evaluated at the horizon, there exist no such neat result for electrical conductivity at the boundary. In this paper we propose an expression for boundary conductivity expressed in terms of geometrical quantities evaluated at the horizon and thermodynamical quantities. We also consider the theory at finite cutoff outside the horizon (arXiv:1006.1902) and give an expression for cutoff dependent electrical conductivity, which interpolates smoothly between horizon conductivity and boundary conductivity . Using the results about the electrical conductivity we gain much insight into the universality of thermal conductivity to viscosity ratio proposed in arXiv:0912.2719.Comment: An appendix added discussing relation between boundary conductivity and universal conductivity of stretched horizon, version to be published in JHE

The Spin of Holographic Electrons at Nonzero Density and Temperature

We study the Green's function of a gauge invariant fermionic operator in a strongly coupled field theory at nonzero temperature and density using a dual gravity description. The gravity model contains a charged black hole in four dimensional anti-de Sitter space and probe charged fermions. In particular, we consider the effects of the spin of these probe fermions on the properties of the Green's function. There exists a spin-orbit coupling between the spin of an electron and the electric field of a Reissner-Nordstrom black hole. On the field theory side, this coupling leads to a Rashba like dispersion relation. We also study the effects of spin on the damping term in the dispersion relation by considering how the spin affects the placement of the fermionic quasinormal modes in the complex frequency plane in a WKB limit. An appendix contains some exact solutions of the Dirac equation in terms of Heun polynomials.Comment: 27 pages, 11 figures; v2: minor changes, published versio

Sum rules and three point functions

Sum rules constraining the R-current spectral densities are derived holographically for the case of D3-branes, M2-branes and M5-branes all at finite chemical potentials. In each of the cases the sum rule relates a certain integral of the spectral density over the frequency to terms which depend both on long distance physics, hydrodynamics and short distance physics of the theory. The terms which which depend on the short distance physics result from the presence of certain chiral primaries in the OPE of two R-currents which are turned on at finite chemical potential. Since these sum rules contain information of the OPE they provide an alternate method to obtain the structure constants of the two R-currents and the chiral primary. As a consistency check we show that the 3 point function derived from the sum rule precisely matches with that obtained using Witten diagrams.Comment: 41 page

Anomalous Zero Sound

We show that the anomalous term in the current, recently suggested by Son and Yamamoto, modifies the structure of the zero sound mode in the Fermi liquid in a magnetic field.Comment: 14 pages, 2 figure

The Sound of Topology in the AdS/CFT Correspondence

Using the gauge/gravity correspondence, we study the properties of 2-point correlation functions of finite-temperature strongly coupled gauge field theories, defined on a curved space of general spatial topology with a dual black hole description. We derive approximate asymptotic expressions for the correlation functions and their poles, supported by exact numerical calculations, and study their dependence on the dimension of spacetime and the spatial topology. The asymptotic structure of the correlation functions depends on the relation between the spatial curvature and the temperature, and is noticeable when they are of the same order. In the case of a hyperbolic topology, a specific temperature is identified for which exact analytical solutions exist for all types of perturbations. The asymptotic structure of the correlation functions poles is found to behave in a non-smooth manner when approaching this temperature.Comment: 65 pages, LaTeX, 21 figures, 1 table; fixed a small error in subsection 3.

Refractive index in holographic superconductors

With the probe limit, we investigate the behavior of the electric permittivity and effective magnetic permeability and related optical properties in the s-wave holographic superconductors. In particular, our result shows that unlike the strong coupled systems which admit a gravity dual of charged black holes in the bulk, the electric permittivity and effective magnetic permeability are unable to conspire to bring about the negative Depine-Lakhtakia index at low frequencies, which implies that the negative phase velocity does not appear in the holographic superconductors under such a situation.Comment: JHEP style, 1+15 pages, 11 figures, version to appear in JHE

Bosonic Fractionalisation Transitions

At finite density, charge in holographic systems can be sourced either by explicit matter sources in the bulk or by bulk horizons. In this paper we find bosonic solutions of both types, breaking a global U(1) symmetry in the former case and leaving it unbroken in the latter. Using a minimal bottom-up model we exhibit phase transitions between the two cases, under the influence of a relevant operator in the dual field theory. We also embed solutions and transitions of this type in M-theory, where, holding the theory at constant chemical potential, the cohesive phase is connected to a neutral phase of Schr\"odinger type via a z=2 QCP.Comment: references added. minor changes. version published in JHE