  Anti-de-Sitter space acts as an infra-red cut off for asymptotically free
theories, allowing interpolation between a weakly-coupled small-sized regime
and a strongly-coupled flat-space regime. We scrutinize the interpolation for
theories in two dimensions from the perspective of boundary conformal theories.
We show that the appearance of a singlet marginal operator destabilizes a
gapless phase existing at a small size, triggering a boundary renormalization
group flow to a gapped phase that smoothly connects to flat space. We
conjecture a similar mechanism for confinement in gauge theories.
