  The chiral magnetic effect with a fluctuating chiral imbalance is more
realistic in the evolution of quark-gluon plasma, which reflects the random
gluonic topological transition. Incorporating this dynamics, we calculate the
chiral magnetic current in response to space-time dependent axial gauge
potential and magnetic field in AdS/CFT correspondence. In contrast to
conventional treatment of constant axial chemical potential, the response
function here is the AVV three-point function of the $\mathcal{N}=4$ super
Yang-Mills at strong coupling. Through an iterative solution of the nonlinear
equations of motion in Schwarzschild-AdS$_5$ background, we are able to express
the AVV function in terms of two Heun functions and prove its UV/IR finiteness,
as expected for $\mathcal{N}=4$ super Yang-Mills theory. We found that the
dependence of the chiral magnetic current on a non-constant chiral imbalance is
non-local, different from hydrodynamic approximation, and demonstrates the
subtlety of the infrared limit discovered in field theoretic approach. We
expect our results enrich the understanding of the phenomenology of the chiral
magnetic effect in the context of relativistic heavy ion collisions.
