Universal Charge Diffusion and the Butterfly Effect in Holographic Theories.

We study charge diffusion in holographic scaling theories with a particle-hole symmetry. We show that these theories have a universal regime in which the diffusion constant is given by D_{c}=Cv_{B}^{2}/(2πT), where v_{B} is the velocity of the butterfly effect. The constant of proportionality C depends only on the scaling exponents of the infrared theory. Our results suggest an unexpected connection between transport at strong coupling and quantum chaos.