Quantum deformed magnon kinematics

Abstract

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^{2πi/λ}. 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=2π/\sqrtλ. The interpretation of the boost generator as the corner transfer matrix is briefly discussed.

7 pages. Latex. v2: Misprint corrected. Added references to the previous elliptic uniformization by N. Beisert and the recent one by I. Kostov, D. Serban and D. Volin