  The optical conductivity of the one-band Hubbard model is calculated using
the 'Dynamical Cluster Approximation' implementation of dynamical mean field
theory for parameters appropriate to high temperature copper-oxide
superconductors. The calculation includes vertex corrections and the result
demonstrates their importance. At densities of one electron per site, an
insulating state is found with gap value and above-gap absorption consistent
with measurements. As carriers are added the above gap conductivity rapidly
weakens and a three component structure emerges, with a low frequency 'Drude'
peak, a mid-infrared absorption, and a remnant of the insulating gap. The
mid-infrared feature obtained at intermediate dopings is shown to arise from a
pseudogap structure in the density of states. On further doping the
conductivity evolves to the Drude peak plus weakly frequency dependent tail
structure expected for less strongly correlated metals.
