Abstract
We discuss a phase diagram for a relativistic $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}{U}_{S}(1)$ 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 $\mathrm{SU}(2)$ 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 $\mathrm{SU}(2)$ symmetry from that where the symmetry is unbroken. We review unconventional (Kosterlitz-Thouless type) superconducting properties of the model, upon coupling it to external electromagnetic potentials. We discuss the role of instantons of the unbroken subgroup $U(1)\ensuremath{\in}\mathrm{SU}(2),$ 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 $\mathrm{SU}(2)$ phase, the model may provide an explanation on the appearance of a pseudogap 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 nonperturbative effects (instantons) of the gauge field $U(1)\ensuremath{\in}\mathrm{SU}(2).$
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