Patrick Kerner

Superconductivity from gauge/gravity duality with flavor

Abstract We consider thermal strongly-coupled N = 2 SYM theory with fundamental matter at finite isospin chemical potential. Using gauge/gravity duality, i.e. a probe of two flavor D7-branes embedded in the AdS black hole background, we find a critical temperature at which the system undergoes a second order phase transition. The critical exponent of this transition is one half and coincides with the result from mean field theory. In the thermodynamically favored phase, a flavor current acquires a vev and breaks an Abelian symmetry spontaneously. This new phase shows signatures known from superconductivity, such as an infinite dc conductivity and a gap in the frequency-dependent conductivity. The gravity setup allows for an explicit identification of the degrees of freedom in the dual field theory, as well as for a dual string picture of the condensation process.

Flavor superconductivity from gauge/gravity duality

We give a detailed account and extensions of a holographic flavor supercon- ductivity model which we have proposed recently. The model has an explicit field theory realization as strongly coupled N = 2 Super Yang-Mills theory with fundamental matter at finite temperature and finite isospin chemical potential. Using gauge/gravity duality, i.e. a probe of two flavor D7-branes in the AdS black hole background, we show that the system undergoes a second order phase transition with critical exponent 1/2. The new ground state may be interpreted as a ρ meson superfluid. It shows signatures known from superconductivity, such as an infinite dc conductivity and a gap in the frequency-dependent conductivity. We present a stringy picture of the condensation mechanism in terms of a recombination of strings. We give a detailed account of the evaluation of the non-Abelian Dirac-Born-Infeld action involved using two different methods. Finally we also consider the case of massive flavors and discuss the holographic Meissner-Ochsenfeld effect in our scenario.

On holographic p-wave superfluids with back-reaction

We numerically construct asymptotically Anti-de Sitter charged black hole solutions of (4 + 1)-dimensional SU(2) Einstein-Yang-Mills theory that, for suciently low temperature, develop vector hair. Via gauge-gravity duality, these solutions describe a strongly-coupled conformal eld theory at nite temperature and density that undergoes a phase transition to a superuid state with spontaneously broken rotational symmetry (a p-wave superuid state). The bulk theory has a single free parameter, the ratio of the ve-dimensional gravitational constant to the Yang-Mills coupling, which we denote as . Previous analyses have shown that in the so-called probe limit, where goes to zero and hence the gauge elds are ignored in Einstein’s equation, the transition to the superuid state is second order. We construct fully back-reacted solutions, where is nite and the gauge elds are included in Einstein’s equation, and nd that for values of above a critical value c = 0:365 0:001 in units of the AdS radius, the transition becomes rst order.

Non-universal shear viscosity from Einstein gravity

Abstract A very famous result of gauge/gravity duality is the universality of the ratio of shear viscosity to entropy density in every field theory holographically dual to classical, two-derivative (Einstein) gravity. We present a way to obtain deviation from this universality by breaking the rotational symmetry spontaneously. In anisotropic fluids additional shear modes exist and their corresponding shear viscosities may be non-universal. We confirm this by explicitly calculating the shear viscosities in a transversely isotropic background, a p-wave superfluid, and study its critical behavior. This is a first decisive step towards further applications of gauge/gravity duality to physical systems.

Finite baryon and isospin chemical potential in AdS/CFT with flavor

We investigate the thermodynamics of a thermal field theory in presence of both a baryon and an isospin chemical potential. For this we consider a probe of several D7-branes embedded in the AdS-Schwarzschild black hole background. We determine the structure of the phase diagram and calculate the relevant thermodynamical quantities both in the canonical and in the grand canonical ensemble. We discuss how accidental symmetries present reflect themselves in the phase diagram: In the case of two flavors, for small densities, there is a rotational symmetry in the plane spanned by the baryon and isospin density which breaks down at large densities, leaving a 4 symmetry. Finally, we calculate vector mode spectral functions and determine their dependence on either the baryon or the isospin density. For large densities, a new excitation forms with energy below the known supersymmetric spectrum. Increasing the density further, this excitation becomes unstable. We speculate that this instability indicates a new phase of condensed mesons.

Transport in anisotropic superfluids: a holographic description

A bstractWe study transport phenomena in p-wave superfluids in the context of gauge/gravity duality. Due to the spacetime anisotropy of this system, the tensorial structure of the transport coefficients is non-trivial in contrast to the isotropic case. In particular, there is an additional shear mode which leads to a non-universal value of the shear viscosity even in an Einstein gravity setup. In this paper, we present a complete study of the helicity two and helicity one fluctuation modes. In addition to the non-universal shear viscosity, we also investigate the thermoelectric effect, i.e. the mixing of electric and heat current. Moreover, we also find an additional effect due to the anisotropy, the so-called flexoelectric effect.

Black Hole Instability Induced by a Magnetic Field

In the context of gauge/gravity duality, we find a new black hole instability in asymptotically AdS spaces. On the field theory side, this instability is induced by a magnetic field in the vacuum, in contrast to previous instabilities which occur at finite density. On the gravity side, this corresponds to a spatial component of the gauge field in SU(2) Einstein–Yang–Mills theory, which provides the crucial non-Abelian structure. Our analysis may provide supporting evidence for recent QCD studies of ρ meson condensation induced by a magnetic field.

Towards a holographic realization of Homes’ law

A bstractGauge/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.

Holographic superuidity in imbalanced mixtures

We construct superfluid black hole solutions with two chemical potentials. By analogy with QCD, the two chemical potentials correspond to the baryon and isospin symmetries, respectively. We consider two systems: the back-reacted U(2) Einstein-Yang-Mills theory in 4 + 1 dimensions and the 9 + 1-dimensional D3/D7 brane setup with two coincident D7-brane probes. In the D7-brane model, the identification of baryon and isospin chemical potential is explicit since the dual field theory is explicitly known. Studying the phase diagram, we find in both systems a quantum phase transition at a critical ratio of the two chemical potentials. However the quantum phase transition is different in the two systems: in the D3/D7 brane setup we always find a second order phase transition, while in the Einstein-Yang-Mills theory, depending on the strength of the back-reaction, we obtain a continuous or first order transition. We expect the continuous quantum phase transition to be BKT-like. We comment on the origin of this differing behavior in these apparently very similar models and compare to phenomenological systems.

Quasinormal modes of massive charged flavor branes

We present an analysis and classiffication of vector and scalar fluctuations in a D3/D7-brane setup at finite temperature and baryon density. The system is dual to an