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

References in corpus (61)

• Giant Magnons
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• On String S-matrix, Bound States and TBA
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• String hypothesis for the AdS_5 x S^5 mirror
• On AdS_5 x S^5 String S-matrix
• Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
• A Shortcut to the Q-Operator
• Wrapping at four loops in N=4 SYM
• Quantum Deformations of the One-Dimensional Hubbard Model
• Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics
• On the Hopf algebra structure of the AdS/CFT S-matrix
• The S-matrix of String Bound States
• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
• The Bethe ansatz approach for factorizable centrally extended S-matrices
• The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure
• The magnon kinematics of the AdS/CFT correspondence
• Twist-three at five loops, Bethe Ansatz and wrapping
• Gauss Decomposition of the Yangian Y(gl_{m|n})
• World-sheet scattering in AdS_5 x S^5 at two loops
• Wronskian Solution for AdS/CFT Y-system
• Konishi operator at intermediate coupling
• Surprisingly Simple Spectra
• From Characters to Quantum (Super)Spin Chains via Fusion
• The classical R-matrix of AdS/CFT and its Lie dialgebra structure
• Classical r-matrix of the su(2|2) SYM spin-chain
• A Secret Symmetry of the AdS/CFT S-matrix
• The Classical Exchange Algebra of AdS5 x S5 String Theory
• Schur-Weyl duality as an instrument of Gauge-String duality
• Algebra of transfer-matrices and Yang-Baxter equations on the string worldsheet in AdS(5) x S(5)
• A Yangian Double for the AdS/CFT Classical r-matrix
• Six-Loop Anomalous Dimension of Twist-Three Operators in N=4 SYM
• Towards Baxter equation in supersymmetric Yang-Mills theories
• Bonus Yangian Symmetry for the Planar S-Matrix of N=4 Super Yang-Mills
• The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain
• q-Deformed Supersymmetry and Dynamic Magnon Representations
• Bound States, Yangian Symmetry and Classical r-matrix for the AdS5 x S5 Superstring
• Drinfeld second realization of the quantum affine superalgebras of $D^{(1)}(2,1;x)$ via the Weyl groupoid
• Yangian symmetry of the Y=0 maximal giant graviton
• Bound State Transfer Matrix for AdS5 x S5 Superstring
• Factorized world-sheet scattering in near-flat AdS_5 x S^5
• On the Scattering of Magnon Boundstates
• Yangian Symmetry at Two Loops for the su(2|1) Sector of N=4 SYM
• Yangian Symmetry of Long-Range gl(N) Integrable Spin Chains
• Tensor products of psl(2|2) representations
• Integrability and the AdS/CFT correspondence
• Weakly coupled N=4 Super Yang-Mills and N=6 Chern-Simons theories from u(2|2) Yangian symmetry
• On the commuting charges for the highest dimension SU(2) operators in planar $\mathcal{N}=4$ SYM
• BPS Operators in N=4 SYM: Calogero Models and 2D Fermions
• Universal blocks of the AdS/CFT Scattering Matrix
• Serre Relation and Higher Grade Generators of the AdS/CFT Yangian Symmetry
• Classical Integrability and Super Yangian of Superstring on AdS_5 x S^5
• Yangian symmetry of boundary scattering in AdS/CFT and the explicit form of bound state reflection matrices
• Structure of the string R-matrix
• The Bethe Ansatz for AdS5 x S5 Bound States
• Note on Centrally Extended su(2/2) and Serre Relations
• The high spin expansion of twist sector dimensions: the planar N=4 super Yang-Mills theory