Nonlinear response of the chiral magnetic effect in the D3/D7 holographic model

A bstract We investigate the nonlinear response of the chiral magnetic current to an external magnetic field in a holographic setup. Using the D3/D7 brane system, where the chiral magnetic effect (CME) can be realized by considering rotating probe D7-branes, corresponding to introducing an axial chemical potential, we analyze the current-magnetic field relation beyond the linear regime. Focusing on the critical region between the insulating phase and the CME phase, we find that the chiral magnetic current exhibits a multi-valued dependence on the magnetic field, which originates from the discrete self-similar structure emerging near the critical embedding characterized by a conical singularity of the probe D7-brane. We further study the dynamical stability of the insulating phase near the transition point, and show that the presence of both an axial chemical potential and an external magnetic field cooperatively stabilize the system. We also discuss the thermodynamic stability of the multiple solutions by computing the thermodynamic potential. Our results clarify the interplay between the axial chemical potential and the magnetic field in determining the phase structure and stability of the system, and provide a new perspective on phase transitions associated with the multi-valued structure.