  Quantum transport close to a critical point is a fundamental, but enigmatic
problem due to fluctuations, persisting at all length scales. We report the
scaling of optical conductivity (OC) in the \emph{collisionless} regime ($\hbar
\omega \gg k_B T$) in the vicinity of a relativistic quantum critical point,
separating two-dimensional ($d=2$) massless Dirac fermions from a fully gapped
insulator or superconductor. Close to such critical point gapless fermionic and
bosonic excitations are strongly coupled, leading to a \emph{universal}
suppression of the inter-band OC as well as of the Drude peak (while
maintaining its delta function profile) inside the critical regime, which we
compute to the leading order in $1/N_f$- and $\epsilon$-expansions, where $N_f$
counts fermion flavor number and $\epsilon=3-d$. Correction to the OC at such a
non-Gaussian critical point due to the long-range Coulomb interaction and
generalizations of these scenarios to a strongly interacting three-dimensional
Dirac or Weyl liquid are also presented, which can be tested numerically and
possibly from non-pertubative gauge-gravity duality, for example.
