Instituto de Física Teórica UAM/CSIC (Webpage 2008-2015)

The integrable structure of N=4 SYM and the superstring in AdS_5xS^5 are encoded in a two-body S-matrix. It has been found that the S-matrix has a relatively simple matrix structure and an extremely complicated overall scalar factor the so-called dressing phase. In this talk I would like to show that such a situation is very generic and that in various cases the dressing phase may be reconstructed from the much simpler matrix structure using nested Bethe ansatz.