Publication: The magnon kinematics of the AdS/CFT correspondence
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2003-11
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Int School Advanced Studies
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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.
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© SISSA 2006. It is a pleasure to thank E. López for collaboration along different stages of this work and illuminating discussions. We are also indebted to L. Álvarez-Gaumé for continuous interest as this work evolved. R. H. would also like to thank the organizers of the Albert Einstein Institut workshop on Integrability in Gauge and String Theory for hospitality and a stimulating atmosphere while this work was being completed. The work of C. G. is partially supported by the Spanish DGI contract FPA2003-02877 and CAM project HEPHACOS P-ESP-00346.