Conductivity bound from dirty black holes

TL;DR

This paper establishes a lower bound on dc electrical conductivity in strongly disordered, strongly interacting quantum systems using holographic duality, analyzing black holes with broken translational symmetry.

Contribution

It introduces a holographic method to derive a lower bound on electrical conductivity in disordered quantum field theories with broken translational symmetry.

Findings

Derived a lower bound for electrical conductivity using horizon fluid dynamics.

Applied the generalized Stokes equations to black hole horizons.

Provided insights into transport properties in disordered strongly coupled systems.

Abstract

We propose a lower bound of the dc electrical conductivity in strongly disordered, strongly interacting quantum field theories using holography. We study linear response of black holes with broken translational symmetry in Einstein-Maxwell-dilaton theories of gravity. Using the generalized Stokes equations at the horizon, we derive the lower bound of the electrical conductivity for the dual two dimensional disordered field theory.