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

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 a 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. At fixed temperature, the stationary string complexity growth is independent of the GB coupling, whereas that of moving strings is suppressed by stronger $R^2$ corrections. Finally, the growth rate is shown to increase linearly with temperature, confirming that higher temperatures systematically drive the complexity growth.