  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.
