  We study conformal field theories in two dimensions separated by domain
walls, which preserve at least one Virasoro algebra. We develop tools to study
such domain walls, extending and clarifying the concept of `folding' discussed
in the condensed-matter literature. We analyze the conditions for unbroken
supersymmetry, and discuss the holographic duals in AdS3 when they exist. One
of the interesting observables is the Casimir energy between a wall and an
anti-wall. When these separate free scalar field theories with different
target-space radii, the Casimir energy is given by the dilogarithm function of
the reflection probability. The walls with holographic duals in AdS3 separate
two sigma models, whose target spaces are moduli spaces of Yang-Mills
instantons on T4 or K3. In the supergravity limit, the Casimir energy is
computable as classical energy of a brane that connects the walls through AdS3.
We compare this result with expectations from the sigma-model point of view.
