  The dynamically generated fermion mass is investigated in the flat brane
world with (4+delta)-dimensional bulk space-time, and in the Randall-Sundrum
(RS) brane world. We consider the bulk Yang-Mills theory interacting with the
fermion confined on a four-dimensional brane. Based on the effective theory
below the reduced cutoff scale on the brane, we formulate the Schwinger-Dyson
equation of the brane fermion propagator. By using the improved ladder
approximation we numerically solve the Schwinger-Dyson equation and find that
the dynamical fermion mass is near the reduced cutoff scale on the brane for
the flat brane world with delta >= 3 and for the RS brane world. In RS brane
world KK excited modes of the bulk gauge field localized around the y = pi R
brane and it enhances the dynamical symmetry breaking on the brane. The decay
constant of the fermion and the anti-fermion composite operator can be taken to
be the order of the electroweak scale much smaller than the Planck scale.
Therefore electroweak mass scale can be realized from only the Planck scale in
the RS brane world due to the fermion and the anti-fermion pair condensation.
That is a dynamical realization of Randall-Sundrum model which solves the
weak-Planck hierarchy problem.
