  We work out the action of the SL(2,Z) electric-magnetic duality group for an
insulator with a non-trivial permittivity, permeability and theta-angle. This
theory has recently been proposed to be the correct low-energy effective action
for topological insulators. As applications, we give manifestly SL(2,Z)
covariant expressions for the Faraday rotation at orthogonal incidence at the
interface of two such materials, as well as for the induced magnetic and
electric charges, slightly clarifying the meaning of expressions previously
derived in the literature. We also use electric-magnetic duality to find a
gravitational dual for a strongly coupled version of this theory using the
AdS/CFT correspondence.
