Holographic complexity of anisotropic black branes

TL;DR

This paper investigates how anisotropy in black branes affects the time evolution of holographic complexity, revealing similarities to isotropic cases but with notable differences in initial growth and late-time behavior.

Contribution

It provides the first detailed analysis of holographic complexity dynamics in anisotropic black branes using the CA conjecture, highlighting the impact of anisotropy.

Findings

Anisotropic systems show similar complexity growth patterns to isotropic ones.

Anisotropy shortens the initial constant complexity period.

Pressure differences influence late-time complexity behavior.

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 behaviour of holographic complexity of anisotropic systems shares a lot of similarities with the behaviour 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.