Deconfining Phase Transition in QCD_4 and QED_4 at Finite Temperature

TL;DR

This paper explores the deconfining phase transition in QCD_4 and QED_4 at finite temperature using a topological quantum field theory approach, revealing a geometrical mechanism involving topological objects and gauge choices.

Contribution

It introduces a perturbative deformation of TQFT with a modified MAG to analyze deconfinement, applying dimensional reduction and topological objects to study phase transitions.

Findings

The linear potential behavior is derived via PS dimensional reduction.

The phase structure of QED_4 at high temperature matches lattice results.

QCD with MAG exhibits abelian dominance facilitating deconfinement discussion.

Abstract

We investigate the deconfining phase transition in QCD_4 and QED_4 at finite temperature using a perturbative deformation of topological quantum field theory (TQFT). A modified maximal abelian gauge (MAG) is utilized in the analysis. In this case, we can derive the linear potential studying the 2D theory through Parisi-Sourlas (PS) dimensional reduction. The mechanism of deconfining phase transition is proposed. It is geometrical to discuss the thermal effect on the linear potential. All we have to do is to investigate the behavior of topological objects as such instantons and vortices on a cylinder. This is the great advantage of our scenario. This mechanism is also applied in the case of QED_4. The phase structure at the high temperature of QED is investigated using the Coulomb potential on a cylinder. It coincides with the result in the lattice compact U(1) gauge theory. Also, QCD with MAG has the property called the abelian dominance, which enables us to discuss the deconfinement of QCD_4.