Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings

N = 4 supersymmetric Yang-Mills operators carrying large charges are dual to semiclassical strings in AdS5 × S. The spectrum of anomalous dimensions of very large operators has been calculated solving the Bethe ansatz equations in the thermodynamic limit, and matched to energies of string solitons. We have considered finite size corrections to the Bethe equations, that should correspond to quantum effects on the string side.