Yangians, S-matrices and AdS/CFT

Journal of Physics A Mathematical and Theoretical (Impact Factor: 1.58). 04/2011; 44(26). DOI: 10.1088/1751-8113/44/26/263001
Source: arXiv


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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    ABSTRACT: We study the Yangian of the sl(2|1) Lie superalgebra in a multi-parametric four-dimensional representation. We use Drinfeld's second realization to independently rederive the R-matrix, and to obtain the antiparticle representation, the crossing and the unitarity condition. We consistently apply the Yangian antipode and its inverse to the individual particles involved in the scattering. We explicitly find a scalar factor solving the crossing and unitarity conditions, and study the analytic structure of the resulting dressed R-matrix. The formulas we obtain bear some similarities with those familiar from the study of integrable structures in the AdS/CFT correspondence, although they present obvious crucial differences.
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    ABSTRACT: We give explicitly the reduction of supersymmetries of the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). Further we give the classification of BPS and possibly protected states.
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    ABSTRACT: We present the `Heisenberg picture' of the reflection algebra by explicitly constructing the boundary Yangian symmetry of an AdS/CFT superstring which ends on a boundary with non-trivial degrees of freedom and which preserves the full bulk Lie symmetry algebra. We also consider the spectrum of bulk and boundary states and some automorphisms of the underlying algebras.
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