Transport in strongly coupled field theories

We will briefly review the methods developed to evaluate transport
properties of strongly coupled matter in the framework of the
gauge/gravity duality.  The methods involve evaluating Kubo formulae
via the gauge/gravity duality and comparison of hydrodynamic modes
with `quasi-normal' modes in gravity.  To emphasize the role the
duality has played in understanding transport properties we focus on a
particular parity odd transport coefficient which was discovered first
by examining certain chiral dispersion relations in gravity.  We then
discuss how sum rules for spectral densities can be derived using the
gauge/gravity duality.  The derivation of sum rules in field theories
usually relies on the analytic properties of the Green's function
involved. This translates to stability properties of an appropriate
fluctuation in gravity.  Sum rules derived from the duality could
serve as inputs to constrain spectral functions assumed in lattice
calculations.