  We discuss a phase diagram for a relativistic SU(2) x U_{S}(1) lattice gauge
theory, with emphasis on the formation of a parity-invariant chiral condensate,
in the case when the $U_{S}(1)$ field is infinitely coupled, and the SU(2)
field is moved away from infinite coupling by means of a strong-coupling
expansion. We provide analytical arguments on the existence of (and partially
derive) a critical line in coupling space, separating the phase of broken SU(2)
symmetry from that where the symmetry is unbroken. We review uncoventional
(Kosterlitz-Thouless type) superconducting properties of the model, upon
coupling it to external electromagnetic potentials. We discuss the r\^ole of
instantons of the unbroken subgroup U(1) of SU(2), in eventually destroying
superconductivity under certain circumstances. The model may have applications
to the theory of high-temperature superconductivity. In particular, we argue
that in the regime of the couplings leading to the broken SU(2) phase, the
model may provide an explanation on the appearance of a pseudo-gap phase, lying
between the antiferromagnetic and the superconducting phases. In such a phase,
a fermion mass gap appears in the theory, but there is no phase coherence, due
to the Kosterlitz-Thouless mode of symmetry breaking. The absence of
superconductivity in this phase is attributed to non-perturbative effects
(instantons) of the subgroup U(1) of SU(2).
