Charge Screening and Confinement in Hot 3-D QED

Abstract

We examine the possibility of a confinement-deconfinement phase transition at finite temperature in both parity invariant and topologically massive three-dimensional quantum electrodynamics. We review an argument showing that the Abelian version of the Polyakov loop operator is an order parameter for confinement, even in the presence of dynamical electrons. We show that, in the parity invariant case, where the tree-level Coulomb potential is logarithmic, there is a Berezinskii-Kosterlitz-Thouless transition at a critical temperature ($T_c=e^2/8\pi +\mathcal{O}(e^4/m)$, when the ratio of the electromagnetic coupling and the temperature to the electron mass is small). Above $T_c$ the electric charge is not confined and the system is in a Debye plasma phase, whereas below $T_c$ the electric charges are confined by a logarithmic Coulomb potential, qualitatively described by the tree-level interaction. When there is a topological mass, no matter how small, in a strict sense the theory is not confining at any temperature; the model exhibits a screening phase, analogous to that found in the Schwinger model and two-dimensional QCD with massless adjoint matter. However, if the topological mass is much smaller than the other dimensional parameters, there is a temperature for which the range of the Coulomb interaction changes from the inverse topological mass to the inverse electron mass. We speculate that this is a vestige of the BKT transition of the parity-invariant system, separating regions with screening and deconfining behavior.

32 pages, Latex, 1 figure, few misprints corrected, some points clarified and some references added

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• $1+1$-Dimensional Large $N$ QCD coupled to Adjoint Fermions
• Two Dimensional QCD coupled to Adjoint Matter and String Theory
• Glueball spectrum in a (1+1)-dimensional model for QCD
• Quantum Mechanics of the Vacuum State in Two-Dimensional QCD with Adjoint Fermions
• Asymptotic Behavior of the Correlator for Polyakov Loops
• QED With Unequal Charges: A study of spontaneous Zn symmetry breaking
• Hot Gauge Theories and $Z_N$ Phases
• Z_N Phases in Hot Gauge Theories
• Phase of the Wilson Line
• Deconfinement Transition in Large N Lattice Gauge Theory
• Canonical Chern-Simons Theory and the Braid Group on a Riemann Surface

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• QED${}_3$ on a space-time lattice: compact versus noncompact formulation
• Thermodynamics of theories with sixteen supercharges in non-trivial vacua
• G/G models as the strong coupling limit of topologically massive gauge theory
• Deconfinement Transition for Quarks on a Line
• Dimensional reduction, magnetic flux strings, and domain walls
• On the chiral and deconfinement phase transitions in parity-conserving QED_3 at finite temperature
• Dynamical mass generation in QED${}_3$: A non-perturbative approach
• The effect of geometry on charge confinement in three dimensions