q-Deformed Supersymmetry and Dynamic Magnon Representations

Abstract

It was recently noted that the dispersion relation for the magnons of planar N=4 SYM can be identified with the Casimir of a certain deformation of the Poincare algebra, in which the energy and momentum operators are supplemented by a boost generator J. By considering the relationship between J and su(2|2) x R^2, we derive a q-deformed super-Poincare symmetry algebra of the kinematics. Using this, we show that the dynamic magnon representations may be obtained by boosting from a fixed rest-frame representation. We comment on aspects of the coalgebra structure and some implications for the question of boost-covariance of the S-matrix.

15 pages, LaTeX; (v2) references added

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Cited by in corpus (25)

• The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• On Drinfeld's second realization of the AdS/CFT su(2|2) Yangian
• Classical r-matrix of the su(2|2) SYM spin-chain
• A Secret Symmetry of the AdS/CFT S-matrix
• Yangians, S-matrices and AdS/CFT
• A Yangian Double for the AdS/CFT Classical r-matrix
• The low-energy limit of AdS${}_3$/CFT${}_2$ and its TBA
• On Symmetry Enhancement in the psu(1,1|2) Sector of N=4 SYM
• The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain
• Covariant particle exchange for kappa-deformed theories in 1+1 dimensions
• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• Massless sector of AdS_3 superstrings: a geometric interpretation
• On the multi-spin magnon and spike solutions from membranes
• Structure of the string R-matrix
• Massless $Ad{S}_2$ scattering and Bethe ansatz
• $q$-Poincaré supersymmetry in $Ad{S}_5/CF{T}_4$
• Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities
• 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
• A study of integrable form factors in massless relativistic AdS_3
• The Ising model and planar N=4 Yang-Mills
• Matrix Reduction and the su(2|2) superalgebra in AdS/CFT
• Geometry of Massless Scattering in Integrable Superstring