# Electrons with disorder & something like AdS/CFT duality

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.

• Have you heard of the Sachdev-Ye-Kitaev (SYK) model? It is a model of disordered fermions with emergent conformal invariance which is known to fit in the AdS/CFT duality, with much of the intuition coming from diagrams. You may also be interested in this paper which studies the disordered large-$N$ models using AdS/CFT (among other methods): arxiv.org/abs/1509.02547. I do not know of a relation between the usual non-crossing-approximation and AdS/CFT, but SYK is a very similar idea. – Seth Whitsitt Dec 14 '19 at 5:27

• A disordered liquid refers to spin states, and these may be electrons in a conduction band that act as a fluid, that are entangled, but that have no magnetic order. There are a few materials with this property, such as $PbCuTe_2O_6$ in a Kagome lattice. Copper is fairly prominent in these materials. These have long range entanglements of spins, but also disordering or frustration of spins. This is the closest thing I could think of with respect to electrons with disorder EwD, which honestly I have never heard of before. – Lawrence B. Crowell Aug 25 '19 at 12:31
• @SethWhitsitt you are completeley correct. I have found that there is duality between $N$-component scalar field theory with interaction $u(\phi^i\phi_i)^2$. However, I do know about the "solid-state" description of this duality. I know about SYK and its dualities. – Artem Alexandrov Dec 14 '19 at 9:02