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

TL;DR

This paper investigates how conformal anomalies affect the rate of change of computational complexity in holographic models, finding it to be unaffected, and proposes using Lloyd's bound saturation as a renormalization condition.

Contribution

It extends holographic complexity studies to include conformal anomalies, demonstrating their insensitivity and suggesting a new renormalization approach based on Lloyd's bound.

Findings

Complexity rate change is independent of conformal anomaly.

Lloyd's bound saturation can serve as a renormalization condition.

Results hold for both Mateos-Trancanelli and D'Hoker-Kraus models.

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.