Asymptotic Bethe ansatz from string sigma model on S3×R

We derive the asymptotic Bethe ansatz (AFS equations [G. Arutyunov, S. Frolov, M. Staudacher, Bethe ansatz for quantum strings, JHEP 0410 (2004) 016, hep-th/0406256]) for the string on S3×R sector of AdS5×S5 from the integrable nonhomogeneous dynamical spin chain for the string sigma model proposed in [N. Gromov, V. Kazakov, K. Sakai, P. Vieira, Strings as multi-particle states of quantum sigma-models, hep-th/0603043]. It is clear from the derivation that AFS equations can be viewed only as an effective model describing a certain regime of a more fundamental inhomogeneous spin chain.