Viscosity Bound Violation in the MTZ Black Hole

Abstract

Using the AdS/CFT correspondence, it has been shown that the ratio of shear viscosity to entropy density is bounded from below in strongly coupled field theories with a gravity dual. More recently, this bound has been shown to be grossly violated in novel non-Fermi liquids and the unitary Fermi gas in the presence of superfluid fluctuations above T_c. Nevertheless, a holographic approach to such systems which break the lower bound have been strongly reliant on AdS spacetimes with massive gravitons. In this work, we propose a violation of the viscosity over entropy bound in 3+1 dimensional AdS spacetimes that support stable black hole solutions with non-zero scalar field. Such a black hole is shown to be characterized by a novel phase transition at large negative mass, where the underlying thermodynamics agrees with the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF)-like phase seen in the unitary Fermi gas near Tc and the bound is similarly broken. Such a work paves the way for a holographic description of strongly-entangled quantum fluids at high Reynolds number.