Emergent quantum criticality, Fermi surfaces, and AdS 2

Gravity solutions dual to $d$-dimensional field theories at finite charge density have a near-horizon region, which is ${mathrm{AdS}}_{2}ifmmodetimeselsetexttimesfi{}{mathbb{R}}^{densuremath{-}1}$. The scale invariance of the ${mathrm{AdS}}_{2}$ region implies that at low energies the dual field theory exhibits emergent quantum critical behavior controlled by a ($0+1$)-dimensional conformal field theories (CFT). This interpretation sheds light on recently-discovered holographic descriptions of Fermi surfaces, allowing an analytic understanding of their low-energy excitations. For example, the scaling behavior near the Fermi surfaces is determined by conformal dimensions in the emergent IR CFT. In particular, when the operator is marginal in the IR CFT, the corresponding spectral function is precisely of the “marginal Fermi liquid” form, postulated to describe the optimally doped cuprates.