Complexity growth in a holographic QCD model* *Supported in part by the National Key Research and Development Program of China (2022YFA1604900). This work is also partly supported by the National Natural Science Foundation of China (NSFC) (12275104, 11890711, 11890710, 11735007)

Abstract

In this study, we utilize the complexity-action duality to study the evolution of complexity in a holographic QCD model at finite temperature and chemical potential. By inserting a fundamental string as a probe, we investigated the properties of complexity growth in this Einstein-Maxwell-scalar gravity system, which is affected by the string velocity, chemical potential, and temperature. Our results show that the complexity growth is maximized when the probe string is stationary, and it decreases as the velocity of the string increases. When the string approaches relativistic velocities, the complexity growth always increases monotonically with respect to the chemical potential. Furthermore, we find that the complexity growth can be used to identify phase transitions and crossovers in the model.