  Reduced gauge theories are theories in which while gauge fields propagate in
a bulk, fermion fields are localized on a brane. We study dynamical chiral
symmetry breaking on a 2-brane and a 1-brane in reduced QED_{3+1}, and on a
1-brane in reduced QED_{2+1}. Since, unlike higher dimensional gauge theories,
QED_{3+1} and QED_{2+1} are well defined, their reduced versions can serve as a
laboratory for studying dynamics in a higher dimensional brane world. The
analysis of the Schwinger-Dyson (SD) equations in these theories reveals rich
and quite nontrivial dynamics in which the conformal symmetry and its breakdown
play a crucial role. Explicit solutions of the SD equations in the
near-critical regime are obtained and the character of the corresponding phase
transition is described.
