Insensitivity of the complexity rate of change to the conformal anomaly and Lloyd's bound as a possible renormalization condition

Abstract

We determine the effect on the computational complexity of a conformal anomaly using the Complexity=Action prescription of the gauge/gravity correspondence. To allow the involvement of said anomaly, we extend previous studies to include arbitrary values for the anisotropic parameter and the magnetic field respectively on the Mateos-Trancanelli and the D'Hoker-Kraus holographic models. Our main result is that the rate of change of the computational complexity is independent of the conformal anomaly in both cases. In addition, this allows us to also show that, if so desired, the saturation of Lloyd's bound at infinite time can be used as a renormalization condition.