SO(5)theory of antiferromagnetism and superconductivity

Antiferromagnetism and superconductivity are both fundamental and common states of matter. In many strongly correlated systems, including the high-$T_c$ cuprates, the heavy-fermion compounds, and the organic superconductors, they occur next to each other in the phase diagram and influence each other’s physical properties. The $\mathit{SO}\left(5\right)$ theory unifies these two basic states of matter by a symmetry principle and describes their rich phenomenology through a single low-energy effective model. In this paper, the authors review the framework of the $\mathit{SO}\left(5\right)$ theory and compare it with numerical and experimental results.