The magnon kinematics of the AdS/CFT correspondence

Abstract

The planar dilatation operator of N=4 supersymmetric Yang-Mills is the hamiltonian of an integrable spin chain whose length is allowed to fluctuate. We will identify the dynamics of length fluctuations of planar N=4 Yang-Mills with the existence of an abelian Hopf algebra Z symmetry with non-trivial co-multiplication and antipode. The intertwiner conditions for this Hopf algebra will restrict the allowed magnon irreps to those leading to the magnon dispersion relation. We will discuss magnon kinematics and crossing symmetry on the spectrum of Z. We also consider general features of the underlying Hopf algebra with Z as central Hopf subalgebra, and discuss the giant magnon semiclassical regime.

21 pages, Latex. v2: Minor changes and additional references

References in corpus (9)

• Giant Magnons
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Quantum corrections to the string Bethe ansatz
• On AdS_5 x S^5 String S-matrix
• Magnon Bound States and the AdS/CFT Correspondence
• Dyonic Giant Magnons
• Infinite spin limit of semiclassical string states
• A Universality Test of the Quantum String Bethe Ansatz
• Multispin Giant Magnons

Cited by in corpus (30)

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• The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure
• Gauge invariant finite size spectrum of the giant magnon
• S-matrix for magnons in the D1-D5 system
• 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
• Integrable S-matrices, massive and massless modes and the AdS_2 x S^2 superstring
• The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain
• Covariant particle exchange for kappa-deformed theories in 1+1 dimensions
• q-Deformed Supersymmetry and Dynamic Magnon Representations
• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• Weakly coupled N=4 Super Yang-Mills and N=6 Chern-Simons theories from u(2|2) Yangian symmetry
• 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
• Structure of the string R-matrix
• The Bethe Ansatz for AdS5 x S5 Bound States
• Massless $Ad{S}_2$ scattering and Bethe ansatz
• Boost generator in AdS_3 integrable superstrings for general braiding
• Contracted and expanded integrable structures
• On $Ad{S}_2/CF{T}_1$ transfer matrices, Bethe ansatz and scale invariance
• Matrix Reduction and the su(2|2) superalgebra in AdS/CFT
• Classical Lie Bialgebras for AdS/CFT Integrability by Contraction and Reduction
• A study of integrable form factors in massless relativistic $Ad{S}_2$
• Quantum Spectral Curve for AdS${}_3$/CFT${}_2$: a proposal