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.
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