Article

# Yangians, S-matrices and AdS/CFT

(Impact Factor: 1.58). 04/2011; 44(26). DOI: 10.1088/1751-8113/44/26/263001
Source: arXiv

ABSTRACT

This review is meant to be an account of the properties of the
infinite-dimensional quantum group (specifically, Yangian) symmetry lying
behind the integrability of the AdS/CFT spectral problem. In passing, the
chance is taken to give a concise anthology of basic facts concerning Yangians
and integrable systems, and to store a series of remarks, observations and
proofs the author has collected in a five-year span of research on the subject.
We hope this exercise will be useful for future attempts to study Yangians in
field and string theories, with or without supersymmetry.

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• "The R-matrix depends on the variables ϑ 1 and ϑ 2 only through their difference, consistently with the existence of a shift automorphism of the Yangian. The representations we find in this paper are all of the so-called evaluation type [28] [29]. In such representations, the shift automorphism simply transforms the spectral parameter as u → u + q, where q is a constant independent on the representation. "
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