Complexity growth in a holographic QCD model*

Abstract

In this work, we study the complexity growth in a holographic QCD model at finite temperature and chemical potential in D dimensions according to the complexity equals action conjecture.
By inserting a fundamental string as a probe, we can analyze the properties of complexity growth. In this work, 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 of 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 will decrease 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.