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 Neel phase of the cuprat es corresponds to the chirally broken phase of QCD, and the high-temperatur e 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. T his suggests that the SU(2)(L) circle times SU(2)(R) circle times U(1)(B) c hiral 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) circle times Z( 2) to SO(3)(s) is known to occur in anisotropic antiferromagnets. In these systems the staggered magnetization hops from an easy 3-axis into the 12-pl ane at a critical value of the external magnetic field. Similarly, the phas e transitions in the SO(5) and SO(10) models are flop transitions of a "sup erspin". Despite this fact, a renormalization group flow analysis in 4 - ep silon dimensions indicates that a point with full SO(5) or SO(10) symmetry exists neither in the cuprates nor in QCD.