Induced gravity and universe creation on the domain wall in five-dimensional space-time

We present a model with a strong fermion self-interaction and an induced gravitational interaction in five-dimensional space-time. In the strong-coupling regime, this model develops a spontaneous breaking of translational invariance, which results in localizing light particles on the $(3+1)$-dimensional domain wall embedded in the anti-de Sitter five-dimensional space-time. We obtain the corresponding low-energy effective action and investigate kink-type vacuum solutions in a quasiflat Riemannian metric. We discuss the physics of light particles in $3+1$ dimensions and establish the fundamental relations between the induced gravitational constant and both the curvature in the five-dimensional anti-de Sitter space-time and the Newton gravitational constant of our universe.