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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 Tc 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., Comment: 32 pages, 9 figures and 1 table

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 Tc 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., Comment: 32 pages, 9 figures and 1 table

We use gauge-gravity duality to study the stability of zero-temperature, finite baryon density states of N=4 supersymmetric SU(Nc) Yang-Mills theory coupled to a single massive fundamental-representation N=2 hypermultiplet in the large-Nc and large-coupling limits. In particular, we study the spectrum of mesons. The dual description is a probe D7-brane in anti-de Sitter space with a particular configuration of worldvolume fields. The meson spectrum is dual to the spectrum of fluctuations of worldvolume fields about that configuration. We use a combination of analytical and numerical techniques to compute the spectrum, including a special numerical technique designed to deal with singular points in the fluctuations' equations of motion. Despite circumstantial evidence that the system might be unstable, such as a finite entropy density at zero temperature and the existence of instabilities in similar theories, we find no evidence of any instabilities, at least for the ranges of frequency and momenta that we consider. We discover a pole on the imaginary frequency axis in a scalar meson two-point function, similar to the diffusive mode in the two-point function of a conserved charge., Comment: 40 pages, 7 figures

We use gauge-gravity duality to study the stability of zero-temperature, finite baryon density states of N=4 supersymmetric SU(Nc) Yang-Mills theory coupled to a single massive fundamental-representation N=2 hypermultiplet in the large-Nc and large-coupling limits. In particular, we study the spectrum of mesons. The dual description is a probe D7-brane in anti-de Sitter space with a particular configuration of worldvolume fields. The meson spectrum is dual to the spectrum of fluctuations of worldvolume fields about that configuration. We use a combination of analytical and numerical techniques to compute the spectrum, including a special numerical technique designed to deal with singular points in the fluctuations' equations of motion. Despite circumstantial evidence that the system might be unstable, such as a finite entropy density at zero temperature and the existence of instabilities in similar theories, we find no evidence of any instabilities, at least for the ranges of frequency and momenta that we consider. We discover a pole on the imaginary frequency axis in a scalar meson two-point function, similar to the diffusive mode in the two-point function of a conserved charge., Comment: 40 pages, 7 figures