Fine Structure of String Spectrum in $AdS_5\times S^5$

The spectrum of an infinite spinning string in $AdS_5$ does not precisely match the spectrum of dual gauge theory operators, interpolated to the strong coupling regime with the help of Bethe-ansatz equations. We show that the mismatch is due to interactions in the string $\sigma$-model which cannot be neglected even at asymptotically large 't Hooft coupling.