Flop Transitions in Cuprate and Color Superconductors: From SO(5) to SO(10) Unification?

TL;DR

This paper explores the theoretical possibility of unifying symmetries in cuprate superconductors and QCD, analyzing phase transitions and symmetry enhancements from SO(5) to SO(10) through flop transitions and renormalization group flow.

Contribution

It proposes a unified framework connecting phase transitions in cuprates and QCD via symmetry unification from SO(5) to SO(10) and analyzes the nature of these transitions.

Findings

Symmetry enhancement from SO(2)_s to SO(3)_s occurs in antiferromagnets.

Flop transitions of a 'superspin' characterize phase changes in SO(5) and SO(10) models.

Full SO(5) or SO(10) symmetry points do not exist in the phase diagrams of cuprates or QCD.

Abstract

The phase diagrams of cuprate superconductors and of QCD at non-zero baryon chemical potential are qualitatively similar. The Neel 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 $SU(2)_L \otimes SU(2)_R \otimes U(1)_B$ chiral symmetry of QCD and the $SU(3)_c$ color gauge symmetry may get unified to SO(10). Dynamical enhancement of symmetry from $SO(2)_s \otimes \Z(2)$ 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 $4-\epsilon$ dimensions indicates that a point with full SO(5) or SO(10) symmetry exists neither in the cuprates nor in QCD.