  A Fermi surface coupled to a scalar field can be described in a $1/N$
expansion by choosing the fermion-scalar Yukawa coupling to be random in the
$N$-dimensional flavor space, but invariant under translations. We compute the
conductivity of such a theory in two spatial dimensions for a critical scalar.
We find a Drude contribution, and verify that the proposed $1/\omega^{2/3}$
contribution to the optical conductivity at frequency $\omega$ has vanishing
co-efficient for a convex Fermi surface. We also describe the influence of
impurity scattering of the fermions, and find that while the self energy
resembles a marginal Fermi liquid, the resistivity and optical conductivity
behave like a Fermi liquid.
