Yangians, S-matrices and AdS/CFT

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.

95 pages, pdfLaTeX, 1 figure. This is an author-created, un-copyedited version of an invited topical review accepted for publication in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. v2: fixed sign in (15), added comment about Jacobi identity in footnote 50

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• L operators and Drinfeld's generators
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• Factorizing twists and the universal R-matrix of the Yangian Y(sl_2)
• The high spin expansion of twist sector dimensions: the planar N=4 super Yang-Mills theory
• Yangian Superalgebras in Conformal Field Theory
• Measurement of the KS->gg branching ratio using a pure KS beam with the KLOE detector

Cited by in corpus (26)

• The all-loop integrable spin-chain for strings on AdS_3 x S^3 x T^4: the massive sector
• The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
• Towards integrability for AdS3/CFT2
• Lectures on Yangian Symmetry
• An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction
• Secret Symmetries of Type IIB Superstring Theory on AdS3 x S3 x M4
• Integrable S-matrices, massive and massless modes and the AdS_2 x S^2 superstring
• The RTT-Realization for the Deformed gl(2|2) Yangian
• Yangian Bootstrap for Massive Feynman Integrals
• The S-matrix algebra of the AdS2 X S2 superstring
• Massive Fishnets
• Nonlocal Symmetries, Spectral Parameter and Minimal Surfaces in AdS/CFT
• Representations of centrally extended Lie superalgebra $\mathfrak{psl}(2|2)$
• $q$-Poincaré supersymmetry in $Ad{S}_5/CF{T}_4$
• The Tetrahedron Zamolodchikov Algebra and the AdS5 x S5 S-matrix
• Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs
• Nonlocal Symmetries and Factorized Scattering
• $q$-Poincaré invariance of the $Ad{S}_3/CF{T}_2$ $R$-matrix
• Boost generator in AdS_3 integrable superstrings for general braiding
• On the massless modes of the AdS3/CFT2 integrable systems
• Drinfeld basis for string-inspired Baxter operators
• Group-Theoretical Classification of BPS and Possibly Protected States in D=4 Conformal Supersymmetry
• The Feyn-Structure of Yangian Symmetry
• Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane
• Wilson Loops and Integrability
• Multi-parametric R-matrix for the sl(2|1) Yangian