Semiclassical approach to confinement in three-dimensional gauge theories

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Abstract
The role of semiclassical configurations in inducing linear confinement in three-dimensional gauge theories is examined with the use of lattice models interpolating between compact U(1) and SU(2) gauge theory. The Abelian monopoles responsible for confinement in the U(1) case are seen to evolve into stable non-Abelian 't Hooft-Polyakov monopoles. Analytic semiclassical calculations are performed, using Debye-Hückel theory, for U(1) and compared with the results of simulations, clarifying the role of cooling in exposing the underlying semiclassical structures. A strategy is proposed for quantitative calculations in the non-Abelian case.