Flop transitions in cuprate and color superconductors: From SO(5) to SO(10) unification?

The phase diagrams of cuprate superconductors and of QCD at non-zero baryon chemical potential are qualitatively similar. The Néel phase of the cuprates corresponds to the chirally broken phase of QCD, and the high-temperature superconducting phase corresponds to the color superconducting phase. In the SO(5) theory for the cuprates the SO(3)s spin rotational symmetry and the U(1)em gauge symmetry of electromagnetism are dynamically unified. This suggests that the SU(2)L ⊗ SU(2)R ⊗ U(1)B chiral symmetry of QCD and the SU(3)c color gauge symmetry may get unified to SO(10). Dynamical enhancement of symmetry from SO(2)s ⊗ Z(2) to SO(3)s is known to occur in anisotropic antiferromagnets. In these systems the staggered magnetization flops from an easy 3-axis into the 12-plane at a critical value of the external magnetic field. Similarly, the phase transitions in the SO(5) and SO(10) models are flop transitions of a “superspin”. Despite this fact, a renormalization group flow analysis in 4 — ϵ dimensions indicates that a point with full SO(5) or SO(10) symmetry exists neither in the cuprates nor in QCD.