  We present an SU(4) model of high-temperature superconductivity having many
similarities to dynamical symmetries known to play an important role in
microscopic nuclear structure physics and in elementary particle physics.
Analytical solutions in three dynamical symmetry limits of this model are
found: an SO(4) limit associated with antiferromagnetic order; an SU(2) X SO(3)
limit that may be interpreted as a d-wave pairing condensate; and an SO(5)
limit that may be interpreted as a doorway state between the antiferromagnetic
order and the superconducting order. The model suggests a phase diagram in
qualitative agreement with that observed in the cuprate superconductors. The
relationship between the present model and the SO(5) unification of
superconductivity and antiferromagnetic order proposed by Zhang is discussed.
