Generalized unitarity and the worldsheet S matrix in AdSn ×s n ×m10-2n

Oluf Tang Engelund, Ryan W. McKeown, Radu Roiban

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Abstract

The integrability-based solution of string theories related to AdS n /CFT n-1 dualities relies on the worldsheet S matrix. Using generalized unitarity we construct the terms with logarithmic dependence on external momenta at one- and two-loop order in the world-sheet S matrix for strings in a general integrable worldsheet theory. We also discuss aspects of calculations at higher orders. The S-matrix elements are expressed as sums of integrals with coefficients given in terms of tree-level worldsheet four-point scattering amplitudes. Off-diagonal one-loop rational functions, not determined by two-dimensional unitarity cuts, are fixed by symmetry considerations. They play an important role in the determination of the two-loop logarithmic contributions. We illustrate the general analysis by computing the logarithmic terms in the one- and two-loop four-particle S-matrix elements in the massive worldsheet sectors of string theory in AdS5×S5, AdS4×CP3, AdS3×S 3×S3×S1 and AdS3× S3×T4. We explore the structure of the S matrices and provide explicit evidence for the absence of higher-order logarithms and for the exponentiation of the one-loop dressing phase.

Original languageEnglish (US)
Article number23
JournalJournal of High Energy Physics
Volume2013
Issue number8
DOIs
Publication statusPublished - Jan 1 2013

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All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

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