Electromagnetic response and approximate SO(5) symmetry in high-T-c superconductors

It has been proposed that the effective Hamiltonian describing high T-c sup erconductivity in cuprate materials has an approximate SO(5) symmetry relat ing the superconducting (SC) and antiferromagnetic (AF) phases of these sys tems. We show that robust consequences of this proposal are potentially lar ge optical conductivities and Raman scattering rates in the AF phase, due t o the electromagnetic response of the doubly charged pseudo Goldstone boson s which must exist there. This provides potentially strong constraints on t he properties of the bosons, such as their mass gap and velocity, at any gi ven value of the doping.