I know that consideration of electrons with disorder can be based on Feynman diagrams with disorder lines. In this approach, only non-crossing diagrams are important and give contribution to self-energy function $\Sigma$ and related quantities. Parameter $p_Fl$ plays the crucial role in this statement ($l$ is mean free path) and it is equivalent to $N$-parameter in field theory. Large-$N$ means that only planar diagrams in theory are important. Assumption $p_Fl\gg 1$ is very similar.
My question: is it possible to show duality between theory of electrons with disorder (EwD) and something like AdS theory? I mean that due to the equivalence of EwD and large-$N$ expansion it seems that one can naively expect that there is a theory which will be dual to EwD in weak coupling limit.
May be my question is not so clear but I would be grateful for any comments which can make it more clear.