Inverse anisotropic catalysis and complexity

Abstract

In this work the effect of anisotropy on computational complexity is considered by CA proposal in holographic two-sided black brane dual of a strongly coupled gauge theory. It is shown that due to confinement-deconfinement phase transition there are two different behaviors: by increase in anisotropy there would be an increase in complexity growth rate in small anisotropy and a decreases in the complexity growth rate in large anisotropy. In the extreme case the very large anisotropy leads to the unity of the complexity growth rate and complexity itself, it means that in this case getting the target state from the reference state is reachable by no effort. Moreover, we suggest that $\frac{1}{M}\frac{dC}{dt}$ is a better representation of system degrees of freedom rather than the complexity growth rate $\frac{dC}{dt}$ and show that how it is related to inverse anisotropic catalysis. In addition, we consider the one-sided black brane dual to the quantum quench and showed that increase in anisotropy comes with decrease in complexity regardless of the anisotropy value which is due to the fact that the system do not experience a phase transition.