  It was proposed in arXiv:1008.2944 that, for certain gauge theories with
gravity duals, electrical conductivity at finite chemical potential is
universal. Here we provide a general proof that, when matter stress tensor
satisfies a compact constraint, electrical conductivity is universal. We
further elaborate our result with several conformal as well as non-conformal
gauge theories. We also discuss how boundary conductivity and universal
conductivity of stretched horizon are related.
