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We investigate the deconfining phase transition in QCD_4 and QED_4 at finitetemperature using a perturbative deformation of topological quantum fieldtheory (TQFT). A modified maximal abelian gauge (MAG) is utilized in theanalysis. In this case, we can derive the linear potential studying the 2Dtheory through Parisi-Sourlas (PS) dimensional reduction. The mechanism ofdeconfining phase transition is proposed. It is geometrical to discuss thethermal effect on the linear potential. All we have to do is to investigate thebehavior of topological objects as such instantons and vortices on a cylinder.This is the great advantage of our scenario. This mechanism is also applied inthe case of QED_4. The phase structure at the high temperature of QED isinvestigated using the Coulomb potential on a cylinder. It coincides with theresult in the lattice compact U(1) gauge theory. Also, QCD with MAG has theproperty called the abelian dominance, which enables us to discuss thedeconfinement of QCD_4.Comment: 27 pages, 7 figures, latex, typos corrected, clarifications and  references adde

Deconfining Phase Transition in QCD4 and QED4 at Finite Temperature

Deconfining Phase Transition in QCD₄ and QED₄ at Finite Temperature