  Assuming that the world-sheet sigma-model in the AdS/CFT correspondence is an
integrable {\em quantum} field theory, we deduce that there might be new
corrections to the spin-chain/string Bethe ansatz paradigm. These come from
virtual particles propagating around the circumference of the cylinder and
render Bethe ansatz quantization conditions only approximate. We determine the
nature of these corrections both at weak and at strong coupling in the near BMN
limit, and find that the first corrections behave qualitatively as wrapping
interactions at weak coupling.
