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

It has been proposed that the effective Hamiltonian describing high Tc superconductivity in cuprate materials has an approximate SO(5) symmetry relating the superconducting (SC) and antiferromagnetic (AF) phases of these systems. We show that robust consequences of this proposal are potentially large optical conductivities and Raman scattering rates in the AF phase, due to the electromagnetic response of the doubly charged pseudo Goldstone bosons which must exist there. This provides potentially strong constraints on the properties of the bosons, such as their mass gap and velocity, at any given value of the doping.