  Electrons moving in graphene behave as massless Dirac fermions, and they
exhibit fascinating low-frequency electrical transport phenomena. Their dynamic
response, however, is little known at frequencies above one terahertz (THz).
Such knowledge is important not only for a deeper understanding of the Dirac
electron quantum transport, but also for graphene applications in ultrahigh
speed THz electronics and IR optoelectronics. In this paper, we report the
first measurement of high-frequency conductivity of graphene from THz to mid-IR
at different carrier concentrations. The conductivity exhibits Drude-like
frequency dependence and increases dramatically at THz frequencies, but its
absolute strength is substantially lower than theoretical predictions. This
anomalous reduction of free electron oscillator strength is corroborated by
corresponding changes in graphene interband transitions, as required by the sum
rule. Our surprising observation indicates that many-body effects and Dirac
fermion-impurity interactions beyond current transport theories are important
for Dirac fermion electrical response in graphene.
