  The chiral magnetic effect for space-time dependent chiral imbalance and
magnetic field is explored from AdS/CFT correspondence which relates the AVV
three-point function of the $\mathcal{N}=4$ super Yang-Mills at strong coupling
on the boundary to the Einstein-Maxwell-Chern-Simons theory in the bulk. A
formulation of the AVV three point function in terms of Heun functions is
developed by an iterative solution of the nonlinear equations of motion in
Schwarzschild-AdS$_5$ background, which is free from UV/IR divergence. The
low-momentum expansion reveals non-local response of the vector current to the
chiral imbalance beyond the hydrodynamic approximation and replicates the
subtlety of the infrared limit discovered in field theoretic approach in weak
coupling. The phenomenological implications to the chiral magnetic effect in
the context of relativistic heavy ion collisions are discussed qualitatively.
