Boundary Scattering in 1+1 Dimensions as an Aharonov-Bohm Effect

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 Z2 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.