Dispersoin of the π resonance

We study the dispersion of the $\pi$ resonance in the superconducting state within the projected SO(5) model\cite{project}. Away from the the commensurate momentum, the propagation of the $\pi$ resonance creates phase slips in the superconducting order parameter. This frustration effect leads to a strong dressing of the $\pi$ resonance and a downwards dispersion away from the commensurate wave vector. Based on these results, we argue that the the commensurate resonance and incommensurate magnetic fluctuations in the cuprates are continuously connected.