### 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 AdS_{5}×S^{5}, AdS_{4}×CP^{3}, AdS_{3}×S ^{3}×S^{3}×S^{1} and AdS_{3}× S^{3}×T^{4}. 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 language | English (US) |
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Article number | 23 |

Journal | Journal of High Energy Physics |

Volume | 2013 |

Issue number | 8 |

DOIs | |

Publication status | Published - Jan 1 2013 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

_{n}×s

^{n}×m

^{10-2n}.

*Journal of High Energy Physics*,

*2013*(8), [23]. https://doi.org/10.1007/JHEP08(2013)023