Phase structure of lattice SU(2) x U(S)(1) three-dimensional gauge theory

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).

Note:

51 pages latex, 10 figures incorporated

gauge field theory: SU(2) x U(1)
lattice field theory: action
dimension: 3
critical phenomena
condensation: chiral
expansion: strong coupling
superconductivity
temperature: high
potential: electromagnetic
instanton

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Figures(8)

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