We consider the ultra light pseudo Nambu-Goldstone boson appearing in the late time cosmological phase transition theories as a dark matter candidate. Since it is almost massless, its nature is more wave like than particle like. Hence we apply quantum mechanics to study how they form the galactic halos. Three predictions are made; (1)the mass profile ρ ∼ r −1.6 , (2)there are ripple-like fine structures in rotation curve, (3) the rotation velocity times ripple's wave length is largely galaxy independent. We compare the rotation curves predicted by our theory with the data observed. † Department of Energy under contract DE-FG05-86ER-40272.

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.

We consider a gravity dual description of time dependent, strongly interacting large-N c N = 4 SYM. We regard the gauge theory system as a fluid with shear viscosity. Our fluid is expanding in one direction following the Bjorken's picture that is relevant to RHIC experiments. We obtain the dual geometry at the late time that is consistent with dissipative hydrodynamics. We show that the integration constants that cannot be determined by hydrodynamics are given by looking at the horizon of the dual geometry. Relationship between time dependence of the energy density and bulk singularity is also discussed. *

In the previous work, we investigated the rotation curves of galaxies assuming that the dark matter consists of ultra light boson appearing in ′ late time phase transition' theory. Generalizing this work, we consider the effect of visible matter and classify the types of rotation curves as we vary the fraction of the mass and extention of visible matter. We show that visible matter, in galaxies with flat rotation curves, has mass fraction 2% ∼ 10% and it is confined within the distance fraction 10% ∼ 20%.

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.