Beisert, NiklasHernández Redondo, RafaelLópez, Esperanza2023-06-202023-06-202006-111126-670810.1088/1126-6708/2006/11/070https://hdl.handle.net/20.500.14352/52141© SISSA 2006. We are grateful to A. Donini, N. Dorey, M. García Pérez, A. González-Arroyo, R. Janik, K. Landsteiner, J. Maldacena and especially M. Staudacher for clarifying discussions and comments. The work of N.B. is supported in part by the U.S. National Science Foundation Grant No. PHY02-43680. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The work of E.L. is supported by a Ramón y Cajal contract of MCYT and in part by the Spanish DGI under contracts FPA2003-02877 and FPA2003-04597.We propose an all-order perturbative expression for the dressing phase of the AdS_(5) x S^(5) string S-matrix at strong coupling. Moreover, we are able to sum up large parts of this expression. This allows us to start the investigation of the analytic structure of the phase at finite coupling revealing a few surprising features. The phase obeys all known constraints including the crossing relation and it matches with the known physical data at strong coupling. In particular, we recover the bound states of giant magnons recently found by Hofman and Maldacena as poles of the scattering matrix. At weak coupling our proposal seems to differ with gauge theory. A possible solution to this disagreement is the inclusion of additional pieces in the phase not contributing to crossing, which we also study.engjournal articlehttps://doi.org/10.1088/1126-6708/2006/11/070http://iopscience.iop.org/https://arxiv.org/abs/hep-th/0609044v2open access53Física-Modelos matemáticos