Holographic flavor transport in Schrödinger spacetime

Journal of High Energy Physics (Impact Factor: 5.62). 03/2010; 2010(6):1-32. DOI: 10.1007/JHEP06(2010)012
Source: OAI

ABSTRACT We use gauge-gravity duality to study the transport properties of a finite density of charge carriers in a strongly-coupled
theory with non-relativistic symmetry. The field theory is N = 4 \mathcal{N} = 4 supersymmetric SU(N

) Yang-Mills theory in the limit of large N

and with large ’t Hooft coupling, deformed by an irrelevant operator, coupled to a number N

of massive N = 4 \mathcal{N}{ = 4} supersymmetric hypermultiplets in the fundamental representation of the gauge group, i.e. flavor fields. The irrelevant deformation
breaks the relativistic conformal group down to the Schrödinger group, which has non-relativistic scale invariance with dynamical
exponent z = 2. Introducing a finite baryon number density of the flavor fields provides us with charge carriers. We compute the associated
DC and AC conductivities using the dual gravitational description of probe D7-branes in an asymptotically Schrödinger spacetime.
We generically find that in the infrared the conductivity exhibits scaling with temperature or frequency that is relativistic,
while in the ultraviolet the scalings appear to be non-relativistic with dynamical exponent z = 2, as expected in the presence of the irrelevant deformation.

KeywordsGauge-gravity correspondence-AdS-CFT Correspondence-Brane Dynamics in Gauge Theories

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We consider logarithmic extensions of the correlation and response functions of scalar operators for the systems with aging as well as Schr\"odinger symmetry. Aging is known to be the simplest nonequilibrium phenomena, and its physical significances can be understood by the two-time correlation and response functions. Their logarithmic part is completely fixed by the bulk geometry in terms of the conformal weight of the dual operator and the dual particle number. Motivated by recent experimental realizations of Kardar-Parisi-Zhang universality class in growth phenomena and its subsequent theoretical extension to aging, we investigate our two-time correlation functions out of equilibrium, which show several qualitatively different behaviors depending on the parameters in our theory. They exhibit either growing or aging, i.e. power-law decaying, behaviors for the entire range of our scaling time. Surprisingly, for some parameter ranges, they exhibit growing at early times as well as aging at later times.
    Journal of High Energy Physics 09/2012; 2013(1). · 5.62 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We investigate systematic classifications of low energy and lower dimensional effective holographic theories with Lifshitz and Schr\"odinger scaling symmetries only using metrics in terms of hyperscaling violation ($\theta$) and dynamical ($z$) exponents. Their consistent parameter spaces are constrained by null energy and positive specific heat conditions, whose validity is explicitly checked against a previously known result. From dimensional reductions of many microscopic string solutions, we observe the classifications are tied with the number of scales in the original microscopic theories. Conformal theories do not generate a nontrivial $\theta$ for a simple sphere reduction. Theories with Lifshitz scaling with one scale are completely fixed by $\theta$ and $z$, and have a universal emblackening factor at finite temperature. Dimensional reduction of intersecting M2-M5 requires, we call, spatial anisotropic exponents ($\sharp$), along with $z$=1, $\theta$=0, because of another scale. Theories with Schr\"odinger scaling show similar simple classifications at zero temperature, while require more care due to an additional parameter being a thermodynamic variable at finite temperature.
    Journal of High Energy Physics 10/2012; 2012(11). · 5.62 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, we consider the AdS-Schwarzshild black hole in light-cone coordinates which exhibits non-relativistic z=2 Schrodinger symmetry. Then, we use the $AdS/CFT$ correspondence to investigate the effect of finite-coupling corrections to two important properties of the strange metals which are the Ohmic resistivity and the inverse Hall angle. It is shown that the Ohmic resistivity and inverse Hall angle are linear and quadratic temperature dependent in the case of $\mathcal{R}^4$ corrections, respectively. While in the case of Gauss-Bonnet gravity, we find that the inverse Hall angle is quadratic temperature dependent and the Ohmic conductivity can never be linear temperature dependent.
    European Physical Journal C 08/2012; 73(1). · 5.25 Impact Factor


Available from