  We present an analysis of the canonical structure of the WZW theory with
untwisted conformal boundary conditions. The phase space of the boundary theory
on a strip is shown to coincide with the phase space of the Chern-Simons theory
on a solid cylinder (a disc times a line) with two Wilson lines. This reveals a
new aspect of the relation between two-dimensional boundary conformal field
theories and three-dimensional topological theories. A decomposition of the
Chern-Simons phase space on a punctured disc in terms of the one on a punctured
sphere and of coadjoint orbits of the loop group easily lends itself to
quantization, providing at the same time a quantization of the boundary WZW
model.
