  We identify the leading finite-size (Luscher-type) correction to the energy
of open strings ending on maximal giant gravitons. In particular we obtain the
leading finite size correction at weak 't Hooft coupling and in the planar
limit to the energy of very short vacuum states. These results are shown to
agree with certain 1, 2, 3 and 4-loop dual gauge theory perturbative
calculations, which we also perform.
