Conductivity bound from dirty black holes

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. Keywords: Gauge-string duality, AdS/CMT, Black holes, Strongly disordered and interacting QFT