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, Eq(1, 1). The quantum deformed symmetry algebra is generated by the momentum, energy and boost, with deformation parameter q = e2πi/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 halfperiods. 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/ √ λ . The interpretation of the boost generator as the corner transfer matrix is briefly discussed.