4,240 research outputs found
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
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