Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-01-22
JHEP 0703:108,2007
Physics
High Energy Physics
High Energy Physics - Theory
7 pages. Latex. v2: Misprint corrected. Added references to the previous elliptic uniformization by N. Beisert and the recent
Scientific paper
10.1088/1126-6708/2007/03/108
The dispersion relation for planar N=4 supersymmetric Yang-Mills is identified with the Casimir of a quantum deformed two-dimensional kinematical symmetry, E_q(1,1). The quantum deformed symmetry algebra is generated by the momentum, energy and boost, with deformation parameter q=e^{2\pi i/\lambda}. Representing the boost as the infinitesimal generator for translations on the rapidity space leads to an elliptic uniformization with crossing transformations implemented through translations by the elliptic half-periods. This quantum deformed algebra can be interpreted as the kinematical symmetry of a discrete integrable model with lattice spacing given by the BMN length a=2\pi/\sqrt{\lambda}. The interpretation of the boost generator as the corner transfer matrix is briefly discussed.
Gómez César
Hernandez Rafael
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