Mirror mirror on the wall (on two-dimensional black holes and Liouville theory)

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.