Abstract:We study AC electric (σ), thermoelectric (α), and thermal (κ) conductivities in a holographic model, which is based on 3+1 dimensional Einstein-Maxwell-scalar action. There is momentum relaxation due to massless scalar fields linear to spatial coordinate. The model has three field theory parameters: temperature (T ), chemical potential (µ), and effective impurity (β). At low frequencies, if β < µ, all three AC conductivities (σ, α,κ) exhibit a Drude peak modified by pair creation contribution (coherent metal). The parameters of this modified Drude peak are obtained analytically. In particular, if β µ the relaxation time of electric conductivity approaches to 2 √ 3µ/β 2 and the modified Drude peak becomes a standard Drude peak. If β > µ the shape of peak deviates from the Drude form (incoherent metal). At intermediate frequencies (T < ω < µ), we have analysed numerical data of three conductivities (σ, α,κ) for a wide variety of parameters, searching for scaling laws, which are expected from either experimental results on cuprates superconductors or some holographic models. In the model we study, we find no clear signs of scaling behaviour.

Abstract:We study the thermoelectric conductivities of a strongly correlated system in the presence of a magnetic field by the gauge/gravity duality. We consider a class of Einstein-Maxwell-Dilaton theories with axion fields imposing momentum relaxation. General analytic formulas for the direct current (DC) conductivities and the Nernst signal are derived in terms of the black hole horizon data. For an explicit model study, we analyse in detail the dyonic black hole modified by momentum relaxation. In this model, for small momentum relaxation, the Nernst signal shows a bell-shaped dependence on the magnetic field, which is a feature of the normal phase of cuprates. We compute all alternating current (AC) electric, thermoelectric, and thermal conductivities by numerical analysis and confirm that their zero frequency limits precisely reproduce our analytic DC formulas, which is a non-trivial consistency check of our methods. We discuss the momentum relaxation effects on the conductivities including cyclotron resonance poles.

We explore phases of an N = 2 super Yang-Mills theory at finite quark density by introducing quark chemical potential in a D3-D7 setup. We formulate the thermodynamics of brane embeddings and we find that the density versus chemical potential equation of state has rich structure. This yields two distinct first order phase transitions in a small window of quark density. In order words, there is a new first order phase transition in the region of deconfined quarks. In this new phase, the chemical potential is a decreasing function of the density. We suggest that this might be relevant to the difference in sQGP-wQGP phases of QCD. PACS numbers: Valid PACS appear hereIntroduction: There has been much hope that one might be able to use AdS/CFT [1] to describe the real systems after certain amount of deformations. For example, it has been suggested that the fireball in Relativistic Heavy Ion Collision (RHIC) viewed as a strongly interacting system [2,3], has been studied using dual gravity models [4][5][6][7][8]. There have been many attempts to construct models phenomenologically closer to QCD [9].More recently, there has been renewed interest in N = 2 super Yang-Mills (SYM) systems with quenched fundamental quark flavors studied by using a holographic description with probe D7-branes in the AdS 5 black hole background [10][11][12][13][14][15]. The key observation is that we have confinement of quarks even in the absence of gluon confinement or area law [10]. The phases of this theory are characterized by the brane embeddings: whether the D7-brane touches the black hole horizon (black hole embedding) or not (Minkowski embedding). Different types of embedding lead to different meson spectra.In this letter, we explore the phases of this theory at finite quark density by introducing quark chemical potential along the lines of [16,17]. We will first establish a clear formulation of the thermodynamics of brane embeddings. We find that we need to renormalize the finite chemical potential due to the divergence of the thermodynamic potentials. We will also find that apart from the type of first order phase transition described in [10,11] at zero chemical potential, there is another class of first order phase transition within the black hole embedding category: it is indicated in Fig. 1 as a hopping between two black hole embeddings.Since black hole embeddings correspond to the deconfined phase, we cautiously suggest that this new type of first order phase transitions might be relevant to the difference between sQGP-wQGP in RHIC experiments. In particular, we find that the chemical potential in this new phase is a decreasing function of the density.We emphasize that depending on whether we control the system by the chemical potential (grand canonical ensemble) or by the density (canonical ensemble), the phase diagram is different. In this letter, we present the analysis and the results for the system based on the canonical

Recent experiments have uncovered evidence of the strongly coupled nature of the graphene: the Wiedemann-Franz law is violated by up to a factor of 20 near the charge neutral point. We describe this strongly-coupled plasma by a holographic model in which there are two distinct conserved U(1) currents. We find that our analytic results for the transport coefficients for two current model have a significantly improved match to the density dependence of the experimental data than the models with only one current. The additive structure in the transports coefficients plays an important role. We also suggest the origin of the two currents.

We present a closed framework of AdS/CFT with finite U (1) B -charge chemical potential. We show how the gauge-invariant identification of the chemical potential with the bulk gauge field emerges from the standard AdS/CFT dictionary. Physical importance and necessity of the Minkowski embeddings within the present framework is also shown numerically in the D3-D7 systems. We point out that the D3-D7 model with only the black-hole embeddings does not have the low-temperature and lowchemical-potential region in the grand-canonical ensemble, hence it is incomplete. A physical interpretation that explains these numerical results is also proposed.