Schwinger Effect and Negative Differential Conductivity in Holographic   Models
  The consequences of the Schwinger effect for conductivity is computed for strong coupling systems using holography. The one loop diagram on the flavor brane introduces an $O({\lambda \over N_c})$ imaginary part in the effective action for a Maxwell flavor gauge field. This in turn introduces a real conductivity in an otherwise insulating phase of the boundary theory. Moreover in certain regions of parameter space the differential conductivity is negative. This is computed in the context of the Sakai-Sugimoto model. 
Shankhadeep Chakrabortty and B.Sathiapalan
hep-th