Critical phenomena in the AdS/CFT duality

Abstract

We review black holes with second-order phase transition in string theory (R-charged black holes and holographic superconductors) and review their static and dynamic critical phenomena. Holographic superconductors have conventional mean-field values for static critical exponents, but R-charged black holes have unconventional ones. For dynamic universality class, holographic superconductors belong to model A, and R-charged black holes belong to model B in the classification of Hohenberg and Halperin. The analysis suggests that some black holes do obey the theory of critical phenomena in condensed matter physics.