  The boundary scattering problem in 1+1 dimensional CFT is relevant to a
multitude of areas of physics, ranging from the Kondo effect in condensed
matter theory to tachyon condensation in string theory. Invoking a
correspondence between CFT on 1+1 dimensional manifolds with boundaries and
Chern-Simons gauge theory on 2+1 dimensional Z_2 orbifolds, we show that the
1+1 dimensional conformal boundary scattering problem can be reformulated as an
Aharonov-Bohm effect experienced by chiral edge states moving on a 1+1
dimensional boundary of the corresponding 2+1 dimensional Chern-Simons system.
The secretly topological origin of this physics leads to a new and simple
derivation of the scattering of a massless scalar field on the line interacting
with a sinusoidal boundary potential.
