Black Holes and Nonrelativistic Quantum Systems

We describe black holes in d + 3 dimensions, whose thermodynamic properties correspond to those of a scale-invariant nonrelativistic (d + 1)-dimensional quantum system with a dynamical exponent z = 2. The gravitational model involves a massive Abelian vector field and a scalar field, in addition to the metric. The energy per particle in the dual theory is vertical bar mu vertical bar d/(d + 2) at any temperature (mu is the chemical potential). The ratio of shear viscosity to entropy density is h/4 pi in any dimension d >= 2.