  We present a novel derivation of the duality between the two-dimensional
Euclidean black hole and supersymmetric Liouville theory. We realise these
(1+1)-dimensional conformal field theories on the worldvolume of domain walls
in a (2+1)-dimensional gauge theory. We show that there exist two complementary
descriptions of the domain wall dynamics, resulting in the two mirror conformal
field theories. In particular, effects which are usually attributed to
worldsheet instantons are captured by the classical scattering of domain walls.
