$R^2$ corrections to Complexity Growth with a Probe String

TL;DR

This paper studies how $R^2$ curvature corrections affect the rate of complexity growth in holography by analyzing a probe string in Gauss-Bonnet $AdS$ black branes, revealing velocity-dependent effects.

Contribution

It introduces the analysis of $R^2$ corrections on holographic complexity growth with a probe string, highlighting the velocity-dependent crossover behavior.

Findings

Complexity growth is maximized for stationary strings.

Motion of the string suppresses complexity growth.

A crossover velocity exists where $R^2$ effects switch from enhancing to suppressing complexity.

Abstract

We investigate the effect of $R^2$ corrections on holographic complexity growth within the framework of the Complexity=Action(CA) conjecture. By introducing a probe string into Gauss-Bonnet(GB) $AdS$ black brane background, we analyze the time derivative of the Nambu-Goto(NG) action as the holographic dual to complexity growth. Our results indicate that the complexity growth is maximized for a stationary string and is suppressed by its motion. Significantly, we identify a crossover point at specific string velocity, where the influence of $R^2$ corrections on complexity growth changes. For slow strings, stronger $R^2$ corrections enhance complexity growth, whereas for fast strings they suppress it.