  We investigate finite-size corrections to anomalous dimensions of large-spin
twist-two operators in the planar maximally supersymmetric Yang-Mills theory.
We develop a framework for analysis of these corrections, that is complementary
to the conventional spin-chain approach, by making use of the hole rather than
the magnon picture. From the dual string theory perspective where the
large-spin operator is identified with the Gubser-Klebanov-Polyakov (GKP)
string, our approach is equivalent to constructing the first Luescher
correction to the energy of the GKP string by incorporating the contribution of
virtual excitations propagating on it. It allows us to propose a formula that
controls a particular class of large-spin corrections to the twist-two
anomalous dimension and holds at any value of the coupling constant. Compared
to wrapping corrections computed with magnons propagating on the spin chain,
the finite-size corrections that are encoded in our formalism start at a lower
loop level. Our formalism thus calls for modification of the asymptotic
contributions which are conventionally incorporated within the Asymptotic Bethe
Ansatz. An educated guess allows us to remedy this pitfall and successfully
confront our predictions with known results up to five loop accuracy at weak
coupling. Finally, our formula sheds light on the weak-to-strong coupling
transition for the subleading large-spin corrections under study and confirms
stringy expectations at strong coupling where they are found to be identical to
the first Luescher correction to the vacuum energy of the O(6) sigma model.
