Review of AdS/CFT Integrability, Chapter III.5: Luscher corrections

In integrable quantum field theories the large volume spectrum is given by the Bethe Ansatz. The leading corrections, due to virtual particles circulating around the cylinder, are encoded in so-called Luscher corrections. In order to apply these techniques to the AdS/CFT correspondence one has to generalize these corrections to the case of generic dispersion relations and to multiparticle states. We review these various generalizations and the applications of Luscher's corrections to the study of the worldsheet QFT of the superstring in AdS5xS5 and, consequently, to anomalous dimensions of operators in N=4 SYM theory.