Proof of universality of electrical conductivity at finite chemical potential

TL;DR

This paper proves that electrical conductivity at finite chemical potential is universal in certain gauge theories with gravity duals, under specific conditions on the matter stress tensor, and explores its implications across various theories.

Contribution

It provides a general proof of conductivity universality under a matter stress tensor constraint, extending previous proposals to a broader class of gauge theories.

Findings

Electrical conductivity is universal when matter stress tensor satisfies a compact constraint.

The proof applies to both conformal and non-conformal gauge theories.

Boundary and horizon conductivities are shown to be related.

Abstract

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.