Are strange metals -- metallic states that are not describable by the traditional theory of metals (Landau's Fermi liquid theory) -- described by a quantum critical theory?
There has been a lot of work on quantum criticality and its CFT equivalence with AdS. Take a look at:
String Theory, Quantum Phase Transitions and the Emergent Fermi-Liquid Authors: Mihailo Cubrovic, Jan Zaanen, Koenraad Schalm
Another paper which is less conformal field related is
Quantum Criticality in Heavy Fermion Metals Authors: Philipp Gegenwart, Qimiao Si, Frank Steglich (Submitted on 13 Dec 2007 (v1), last revised 31 Jan 2008 (this version, v2))