Dissecting holographic conductivities

TL;DR

This paper analyzes holographic conductivities with broken translational symmetry, decomposing them into coherent and incoherent parts, and provides a physical explanation for their behavior in the slow momentum relaxation limit.

Contribution

It introduces a novel decomposition of holographic conductivities into coherent and incoherent contributions, advancing the understanding of charged hydrodynamics with slow momentum relaxation.

Findings

Decomposition of conductivities into coherent and incoherent parts.

Physical explanation for conductivities in slow momentum relaxation limit.

Consistency with hydrodynamic properties in translationally invariant limit.

Abstract

The DC thermoelectric conductivities of holographic systems in which translational symmetry is broken can be efficiently computed in terms of the near-horizon data of the dual black hole. By calculating the frequency dependent conductivities to the first subleading order in the momentum relaxation rate, we give a physical explanation for these conductivities in the simplest such example, in the limit of slow momentum relaxation. Specifically, we decompose each conductivity into the sum of a coherent contribution due to momentum relaxation and an incoherent contribution, due to intrinsic current relaxation. This decomposition is different from those previously proposed, and is consistent with the known hydrodynamic properties in the translationally invariant limit. This is the first step towards constructing a consistent theory of charged hydrodynamics with slow momentum relaxation.