Quantum Criticality via Magnetic Branes

Abstract

Holographic methods are used to investigate the low temperature limit, including quantum critical behavior, of strongly coupled 4-dimensional gauge theories in the presence of an external magnetic field, and finite charge density. In addition to the metric, the dual gravity theory contains a Maxwell field with Chern-Simons coupling. In the absence of charge, the magnetic field induces an RG flow to an infrared AdS$_3 \times {\bf R}^2$ geometry, which is dual to a 2-dimensional CFT representing strongly interacting fermions in the lowest Landau level. Two asymptotic Virasoro algebras and one chiral Kac-Moody algebra arise as {\sl emergent symmetries} in the IR. Including a nonzero charge density reveals a quantum critical point when the magnetic field reaches a critical value whose scale is set by the charge density. The critical theory is probed by the study of long-distance correlation functions of the boundary stress tensor and current. All quantities of major physical interest in this system, such as critical exponents and scaling functions, can be computed analytically. We also study an asymptotically AdS$_6$ system whose magnetic field induced quantum critical point is governed by a IR Lifshitz geometry, holographically dual to a D=2+1 field theory. The behavior of these holographic theories shares important similarities with that of real world quantum critical systems obtained by tuning a magnetic field, and may be relevant to materials such as Strontium Ruthenates.Comment: To appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye