  We describe general features of frequency-dependent charge transport near
strongly interacting quantum critical points in 2+1 dimensions. The simplest
description using the AdS/CFT correspondence leads to a self-dual
Einstein-Maxwell theory on AdS_4, which fixes the conductivity at a
frequency-independent self-dual value. We describe the general structure of
higher-derivative corrections to the Einstein-Maxwell theory, and compute their
implications for the frequency dependence of the quantum-critical conductivity.
We show that physical consistency conditions on the higher-derivative terms
allow only a limited frequency dependence in the conductivity. The frequency
dependence is amenable to a physical interpretation using transport of either
particle-like or vortex-like excitations.
