  We use AdS_5 x S^5 superstring sigma model perturbation theory to compute the
leading one-loop corrections to the dispersion relations of the excitations
near a long spinning string in AdS. This investigation is partially motivated
by the OPE-based approach to the computation of the expectation value of null
polygonal Wilson loops suggested in arXiv:1006.2788. Our results are in partial
agreement with the recent asymptotic Bethe ansatz computation in
arXiv:1010.5237. In particular, we find that the heaviest AdS mode (absent in
the ABA approach) is stable and has a corrected one-loop dispersion relation
similar to the other massive modes. Its stability might hold also at the
next-to-leading order as we suggest using a unitarity-based argument.
