Slow Relaxation and Diffusion in Holographic Quantum Critical Phases.

The dissipative dynamics of strongly interacting systems are often characterized by the timescale set by the inverse temperature τ_{P}∼ℏ/(k_{B}T). We show that near a class of strongly interacting quantum critical points that arise in the infrared limit of translationally invariant holographic theories, there is a collective excitation (a quasinormal mode of the dual black hole spacetime) whose lifetime τ_{eq} is parametrically longer than τ_{P}: τ_{eq}≫T^{-1}. The lifetime is enhanced due to its dependence on a dangerously irrelevant coupling that breaks the particle-hole symmetry and the invariance under Lorentz boosts of the quantum critical point.