We discuss the general features of charge transport of quantum critical points described by CFTs in 2+1D. Our main tool is the AdS/CFT correspondence, but we will make connections to standard field theory results and to recent quantum Monte Carlo data. We emphasize the importance of poles and zeros of the response functions. In the holographic setting, these are the discrete quasinormal modes of a black hole/brane; they map to the excitations of the CFT. We further describe the role of particle-vortex or S-duality on the conductivity, which is argued to obey two powerful sum rules.
References (with S. Sachdev): arXiv:1210.4166 (PRB 12); arXiv:1302.0847 (PRB 13)