Abstract

In a clean quantum critical metal, and in the absence of umklapp, most d.c. conductivities are formally infinite due to momentum conservation. However, there is a particular combination of the charge and heat currents which has a finite, universal conductivity. In this talk, I will describe the physics of this conductivity in quantum critical metals obtained by charge doping a strongly interacting conformal field theory. I will show that it satisfies an Einstein relation and controls the diffusivity of a conserved charge in the metal. I will compute it in a class of theories with holographic gravitational duals. Finally, I will show how its temperature scaling of depends on certain critical exponents characterizing the quantum critical metal. The holographic results are found to be reproduced by the scaling analysis, with the charge density operator becoming marginal in the emergent low energy quantum critical theory.