Induced Field Theory on the Brane World

We show how the gravity, gauge, and matter fields are induced on dynamically localized brane world (domain wall, vortex etc.). Solitonic solutions localized on a curved brane in certain field theories in higher dimensions are given in terms of gravity, gauge and extrinsic curvature fields of the brane. Then we deduce the effective field theory on the brane in terms of those fields and the quantum fluctuations of the solitonic solution. The gravity, gauge and the extrinsic curvature fields should obey the Gauss-Codazzi-Ricci equation in addition to their own equations of motion.