Quantum corrections to the string Bethe ansatz
  One-loop corrections to the energy of semiclassical rotating strings contain both analytic and non-analytic terms in the 't Hooft coupling. Analytic contributions agree with the prediction from the string Bethe ansatz based on the classical S-matrix, but in order to include non-analytic contributions quantum corrections are required. We find a general expression for the first quantum correction to the string Bethe ansatz. 
Rafael Hernandez, Esperanza Lopez