  In the recent paper arXiv:1010.5009, Maldacena et al. derive the two loop
expressions for polygonal Wilson loops expectation values, or MHV amplitudes,
by writing them as sums over exchanges of intermediate free particles. The
spectrum of excitations of the flux tube between two null Wilson lines can be
viewed as the spectrum of excitations around the infinite spin limit of finite
twist operators in the sl(2) sector of N=4 SYM or the Gubser-Klebanov-Polyakov
(GKP) string. This regime can be captured exploiting integrability and assuming
that wrapping corrections are negligible compared to asymptotic Bethe Ansatz
contributions. This assumption holds true for the N=4 SYM background GKP
string, but deserves further analysis for excited states. Here, we investigate
GKP cousins by considering various classes of (generalized) twist operators in
beta-deformed N=4 SYM and ABJM theory. We show that the Y-system of
Gromov-Kazakov-Vieira easily leads to accurate large spin expansions of the
wrapping correction at lowest order in weak-coupling perturbation theory. As a
byproduct, we confirm that wrapping corrections are subleading in all the
considered cases.
