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 awa
y 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).
We suggest that a spin-charge separating ansatz, leading to non-Abelian $SU(2) otimes U_S(1)$ gauge symmetries in doped antiferromagnets, proposed earlier as a way of describing Kosterlitz-Thouless superconducting gaps at the nodes of the gap of d-wa
ve (high-T_c) superconductors, may also lead to a pseudogap phase, characterised by the formation of (non-superconducting) pairing and the absence of phase coherence. The crucial assumption is again the presence of electrically charged Dirac fermionic excitations (holons) about the points of the (putative) fermi surface in the pertinent phase of the superconductor. We present arguments in support of the r^ole of non-perturbative effects (instantons) on the onset of the pseudogap phase. As a means of probing such gauge interactions experimentally, we perform a study of the scaling of the thermal conductivity with an externally-applied magnetic field, in certain effective models involving gauge and/or four-fermion (contact) interactions.
We perform a lattice study, in the quenched approximation, of dynamical mass generation in a system of relativistic (Dirac) fermions, coupled to an Abelian gauge field in (2+1)-dimensions, in the presence of an external (constant) magnetic field, per
pendicular to the spatial planes. It is shown that a strong magnetic field catalyzes chiral symmetry breaking, in agreement with results in the continuum. The r^ole of the higher-Landau poles in inducing a critical temperature above which the phenomenon disappears is pointed out. We also discuss the implications of this model on the opening of a gap in doped antiferromagnetic superconductors.
