Strange Metals and the AdS/CFT Correspondence

Abstract

I begin with a review of quantum impurity models in condensed matter physics, in which a localized spin degree of freedom is coupled to an interacting conformal field theory in (d) = 2 spatial dimensions. Their properties are similar to those of supersymmetric generalizations which can be solved by the AdS/CFT correspondence; the low energy limit of the latter models is described by a (AdS_2) geometry. Then I turn to Kondo lattice models, which can be described by a mean- field theory obtained by a mapping to a quantum impurity coupled to a self-consistent environment. Such a theory yields a 'fractionalized Fermi liquid' phase of conduction electrons coupled to a critical spin liquid state, and is an attractive mean-field theory of strange metals. The recent holographic description of strange metals with a (AdS_2 \times R^2) geometry is argued to be related to such mean-field solutions of Kondo lattice models.