q-Deformed Supersymmetry and Dynamic Magnon Representations

Understand

It was recently noted that the dispersion relation for the magnons of planar N=4 SYM can be identified with the Casimir of a certain deformation of the Poincare algebra, in which the energy and momentum operators are supplemented by a boost generator J.

• By considering the relationship between J and su(2|2) x R^2, we derive a q-deformed super-Poincare symmetry algebra of the kinematics.
• Using this, we show that the dynamic magnon representations may be obtained by boosting from a fixed rest-frame representation.
• We comment on aspects of the coalgebra structure and some implications for the question of boost-covariance of the S-matrix.