A note on conductivity and charge diffusion in holographic flavour systems

TL;DR

This paper investigates charge diffusion and conductivity in a holographic Dp/Dq system, extending the membrane paradigm and confirming the Einstein relation at finite chemical potential through numerical analysis.

Contribution

It provides a new derivation of conductivity and diffusion results in holographic flavor systems, generalizing the membrane paradigm to finite chemical potential.

Findings

Supports the validity of the Einstein relation at finite chemical potential

Numerical analysis of D3/D7 system confirms theoretical predictions

Extends membrane paradigm to supersymmetric Yang-Mills theories with flavors

Abstract

We analyze the charge diffusion and conductivity in a Dp/Dq holographic setup that is dual to a supersymmetric Yang-Mills theory in p+1 dimensions with N_f<< N_c flavour degrees of freedom at finite temperature and nonvanishing U(1) baryon number chemical potential. We provide a new derivation of the results that generalize the membrane paradigm to the present context. We perform a numerical analysis in the particular case of the D3/D7 flavor system. The results obtained support the validity of the Einstein relation at finite chemical potential.