Y-system and quasi-classical strings

Recently Kazakov, Vieira and the author conjectured the Y-system set of equations describing the planar spectrum of AdS/CFT. In this paper we solve the Y-system equations in the strong coupling scaling limit. We show that the quasi-classical spectrum of string moving inside AdS3 × S1 matches precisely with the prediction of the Y-system. Thus the Y-system, unlike the asymptotic Bethe ansatz, describes correctly the spectrum of one-loop string energies including all exponential finite size corrections. This gives a very non-trivial further support in favor of the conjecture.