Holographic Conductivity in Disordered Systems

The main purpose of this paper is to holographically study the behavior of conductivity in 2+1 dimensional disordered systems. We analyze probe D-brane systems in AdS/CFT with random closed string and open string background fields. We give a prescription of calculating the DC conductivity holographically in disordered systems. In particular, we find an analytical formula of the conductivity in the presence of codimension one randomness. We also systematically study the AC conductivity in various probe brane setups without disorder and find analogues of Mott insulators.