Gauge/gravity duality applied to condensed matter systems

Gauge/gravity duality has proved to be a very successful tool for describing strongly coupled systems in particle physics and heavy ion physics. The application of the gauge/gravity duality to quantum matter is a promising candidate to explain questions concerning non-zero temperature dynamics and transport coefficients. To a large extent, the success of applications of gauge/gravity duality to the quark-gluon plasma is founded on the derivation of a universal result, the famous ratio of shear viscosity and entropy density. As a base for applications to condensed matter physics, it is highly desirable to have a similar universal relation in this context as well. A candidate for such a universal law is given by Homes' law : High T c superconductors, as well as some conventional superconductors, exhibit a universal scaling relation between the superfluid density at zero temperature and the conductivity at the critical temperature times the critical temperature itself. In this work we describe progress in employing the models of holographic superconductors to realize Homes' law and to find a universal relation governing strongly correlated quantum matter. We calculate diffusive processes, including the backreaction of the gravitational matter fields on the geometry. We consider both holographic s-wave and p-wave superconductors. We show that a particular form of Homes' law holds in the absence of backreaction. Moreover, we suggest further steps to be taken for holographically realizing Homes' law more generally in the presence of backreaction.

Section: Introductionmentioning

confidence: 99%

Towards a holographic realization of Homes’ law

Erdmenger

Kerner

Müller

2012

“…The background geometry corresponding to homogeneous boundary conditions on g µν and φ can be found by solving Einstein's equations for the metric in Eq. (24) which take the form:Ḃ = − 1 6φ 2 ,…”

Section: Einstein's Equations and One-point Functionsmentioning

confidence: 99%

“…The discovery of the AdS/CFT holographic correspondence [16][17][18] has opened new possibilities to study thermodynamics and transport in strongly coupled theories (for reviews see [19][20][21][22][23][24][25]). Although not yet directly applicable to QCD, at least until we know its holographic dual, these methods allow one to study generic properties of the strongly coupled plasmas using model theories, such as N = 4 SUSY YM, or holographic models which incorporate QCD-like features such as confinement.…”

Section: Introductionmentioning

confidence: 99%

Bulk spectral function sum rule in QCD-like theories with a holographic dual

Hohler

Stephanov

2011

We derive the sum rule for the spectral function of the stress-energy tensor in the bulk (uniform dilatation) channel in a general class of strongly coupled field theories. This class includes theories holographically dual to a theory of gravity coupled to a single scalar field, representing the operator of the scale anomaly. In the limit when the operator becomes marginal, the sum rule coincides with that in QCD. Using the holographic model, we verify explicitly the cancellation between large and small frequency contributions to the spectral integral required to satisfy the sum rule in such QCD-like theories.

“…In a separate development, there has been considerable interest in using the AdS/CFT correspondence to build models of condensed matter physics (for reviews, see [2,3,4,5]). The Schrödinger spacetime, formulated in [6,7] and embedded in string theory in [8,9,10], is of interest due to its isometry group matching the non-relativistic conformal symmetry [11] of certain ultracold gases at unitarity, although a number of issues with the application of the geometry remain (for a recent discussion of some aspects, see for example [12,13,14]).…”

Section: Introductionmentioning

confidence: 99%

The Gödel-Schrödinger spacetime and stringy chronology protection

Brown

DeWolfe

2012

We show that the null Melvin map applied to a rotational isometry of global anti-de Sitter space produces a spacetime with properties analogous to both the Gödel and Schrödinger geometries. The isometry group of this Gödel-Schrödinger spacetime is appropriate to provide a holographic dual for the same non-relativistic conformal theory as the ordinary Schrödinger geometry, but defined on a sphere. This spacetime also possesses closed timelike curves outside a certain critical radius. We show that a holographic preferred screen for an observer at the origin sits at an interior radius, suggesting that a holographic dual description would only require the chronologically consistent region. Additionally, giant graviton probe branes experience repulsontype instabilities in the acausal region, suggesting a condensation of branes will modify the pathological part of the geometry to remove the closed timelike curves.