  In this paper we study particle-vortex duality and the effect of theta terms
from the point of view of AdS/CMT constructions. We can construct the duality
in 2+1 dimensional field theories with or without a Chern-Simons term, and
derive an effect on conductivities, when the action is viewed as a response
action. We can find its effect on 3+1 dimensional theories, with or without a
theta term, coupled to gravity in asymptotically AdS space, and derive the
resulting effect on conductivities defined in the spirit of AdS/CFT. AdS/CFT
then relates the 2+1 dimensional and the 3+1 dimensional cases naturally.
Quantum gravity corrections, as well as more general effective actions for the
abelian vector, can be treated similarly. We can use the fluid/gravity
correspondence, and the membrane paradigm, to define shear and bulk viscosities
$\eta$ and $\zeta$ for a gravity plus abelian vector plus scalar system near a
black hole, and define the effect of the S-duality on it.
