Abstract. We propose an all-order perturbative expression for the dressing phase of the AdS₅ × S⁵ 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.

Key words: Sigma Models; AdS-CFT Correspondence; Integrable Field Theories; Exact S-Matrix

E-print number: hep-th/0609044
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Received 27 October 2006, accepted for publication 1 November 2006
Published 24 November 2006