SO(5) invariance and effective field theory for high-Tcsuperconductors

We set up the effective field theories which describe the SO(5)-invariant picture of the high-$T_c$ cuprates in various regimes. We use these to get quantitative conclusions concerning the size of SO(5) breaking effects. We consider two applications in detail: (i) the thermodynamic free energy, which describes the phase diagram and critical behavior, and (ii) the Lagrangian governing the interactions of the pseudo-Goldstone bosons with each other and with the electron quasiparticles deep within the ordered phases. We use these effective theories to obtain predictions for the critical behavior near the possible bicritical point and the pseudo-Goldstone boson dispersion relations, as well as some preliminary results concerning their contribution to response functions. We systematically identify which predictions are independent of the microscopic details of the underlying electron dynamics, and which depend on more model-dependent assumptions.