Holographic complexity of anisotropic black branes

Abstract

We use the complexity=action (CA) conjecture to study the full-time dependence of holographic complexity in anisotropic black branes. We find that the time behavior of holographic complexity of anisotropic systems shares a lot of similarities with the behavior observed in isotropic systems. In particular, the holographic complexity remains constant for some initial period, and then it starts to change so that the complexity growth rate violates the Lloyd's bound at initial times, and approaches this bound from above at later times. Compared with isotropic systems at the same temperature, the anisotropy reduces the initial period in which the complexity is constant and increases the rate of change of complexity. At late times the difference between the isotropic and anisotropic results is proportional to the pressure difference in the transverse and longitudinal directions. In the case of charged anisotropic black branes, we find that the inclusion of a Maxwell boundary term is necessary to have consistent results. Moreover, the resulting complexity growth rate does not saturate the Lloyd's bound at late times.