On wrapping corrections to GKP-like operators

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. Assuming that the Y-system of Gromov-Kazakov-Vieira correctly reproduces the wrapping corrections, we show that it easily leads to accurate large spin expansions at lowest order in weak-coupling perturbation theory. As a byproduct, we confirm these corrections are subleading in all the considered cases.