  A gauge theory with 4 physical dimensions can be consistently expressed as a
renormalizable topological quantum field theory in 5 dimensions. We extend the
symmetries in the 5-dimensional framework to include not only a topological
BRST operator S that encodes the invisibility of the "bulk" (the fifth
dimension), but also a gauge BRST operator W that encodes gauge-invariance and
selects observables. These symmetries provide a rich structure of Ward
identities which assure the renormalizability of the theory, including
non-renormalization theorems. The 5-dimensional approach considerably
simplifies conceptual questions such as for instance the Gribov phenomenon and
fermion doubling. A confinement scenario in the 5-dimensional framework is
sketched. We detail the five-dimensional mechanism of anomalies, and we exhibit
a natural lattice discretization that is free of fermion doubling.
