An Exceptional Algebraic Origin of the AdS/CFT Yangian Symmetry

Abstract

In the su(2|2) spin chain motivated by the AdS/CFT correspondence, a novel symmetry extending the superalgebra su(2|2) into u(2|2) was found. We pursue the origin of this symmetry in the exceptional superalgebra d(2,1;epsilon), which recovers su(2|2) when the parameter epsilon is taken to zero. Especially, we rederive the Yangian symmetries of the AdS/CFT spin chain using the exceptional superalgebra and find that the epsilon-correction corresponds to the novel symmetry. Also, we reproduce the non-canonical classical r-matrix of the AdS/CFT spin chain expressed with this symmetry from the canonical one of the exceptional algebra.

20 pages, 3 figures, v3: minor changes and references added

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Cited by in corpus (23)

• The S-matrix of String Bound States
• The Bound State S-Matrix for AdS5 x S5 Superstring
• On Drinfeld's second realization of the AdS/CFT su(2|2) Yangian
• Monodromy Bootstrap for SU(2|2) Quantum Spectral Curves: From Hubbard model to AdS3/CFT2
• Yangians, S-matrices and AdS/CFT
• Yangian symmetry of the Y=0 maximal giant graviton
• The Bound State S-matrix of the Deformed Hubbard Chain
• Secret Symmetries in AdS/CFT
• The su(2|3) Undynamic Spin Chain
• Universal blocks of the AdS/CFT Scattering Matrix
• Serre Relation and Higher Grade Generators of the AdS/CFT Yangian Symmetry
• Nonlocal Charges for Bonus Yangian Symmetries of Super-Yang-Mills
• Maximally extended sl(2|2), q-deformed d(2,1;epsilon) and 3D kappa-Poincaré
• Structure of the string R-matrix
• Particle in a self-dual dyon background: hidden free nature, and exotic superconformal symmetry
• Review of AdS/CFT Integrability, Chapter VI.2: Yangian Algebra
• The secret symmetries of the AdS/CFT reflection matrices
• The Yangian of sl(n|m) and the universal R-matrix
• Reflection algebra, Yangian symmetry and bound-states in AdS/CFT
• Classical Lie Bialgebras for AdS/CFT Integrability by Contraction and Reduction
• Spin-chain with PSU(2|2)xU(1)^3 and Non-linear Sigma-model with D(2,1;gamma)
• Free field realization of the exceptional current superalgebra $\hat{D(2,1;\a)}_k$
• On matrix realizations of the Lie superalgebra D(2, 1 ; α)