RG flow of transport quantities

Abstract

The RG flow equation of various transport quantities are studied in arbitrary spacetime dimensions, in the fixed as well as fluctuating background geometry both for the Maxwellian and DBI type of actions. The regularity condition on the flow equation of the conductivity at the horizon for the DBI action reproduces naturally the leading order result of {\it Hartnoll et al.}, [{\it JHEP}, {\bf 04}, 120 (2010)]. Motivated by the result of {\it van der Marel et al.}, [{\it science}, {\bf 425}, 271 (2003], we studied, analytically, the conductivity versus frequency plane by dividing it into three distinct parts: $\omega <T,\omega >T$ and $\omega >>T$. In order to compare, we choose 3+1 dimensional bulk spacetime for the computation of the conductivity. In the $\omega <T$ range, the conductivity does not show up the Drude like form in any spacetime dimensions. In the $\omega >T$ range and staying away from the horizon, for the DBI action with unit dynamical exponent, non-zero magnetic field and charge density, the conductivity goes as ${\omega }^{-2/3}$, whereas the phase of the conductivity, goes as, $ArcTan(Im{\sigma }^{xx}/Re{\sigma }^{xx})=\pi /6$ and $ArcTan(Im{\sigma }^{xy}/Re{\sigma }^{xy})=-\pi /3$. There exists a universal quantity at the horizon that is the phase angle of conductivity, which either vanishes or an integral multiple of $\pi$. Furthermore, we calculate the temperature dependence to the thermoelectric and the thermal conductivity at the horizon. The charge diffusion constant for the DBI action is studied.

1+68 pages, 12 figures and 4 appendices; V2: The charge diffusion constant is calculated for arbitrary spacetime dimensions and related references added; v3: Connection with the RG flow of 1010.4036 is made; v4: Several corrections, typos fixed and a ref. added

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• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
• Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
• Quantum critical transport, duality, and M-theory
• Hall conductivity from dyonic black holes
• Ohm's Law at strong coupling: S duality and the cyclotron resonance
• Impure AdS/CFT
• The gravity dual to a quantum critical point with spontaneous symmetry breaking
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Cited by in corpus (3)

• Holographic Flow of Anomalous Transport Coefficients
• Thermodynamics of Einstein-DBI System
• RG flow of AC Conductivity in Soft Wall Model of QCD