Vortices and confinement in hot and cold D = (2+1) gauge theories

We calculate the variation with temperature of the vortex free energy in D=2+1 SU(2) lattice gauge theories. We do so both above and below the deconfining transition at T=Tc. We find that this quantity is zero at all T for large enough volumes. For TTc it is consistent with the conventional expectation of `spatial' linear confinement. In small spatial volumes this quantity is shown to be non-zero. The way it decreases to zero with increasing volume is shown to be controlled by the (spatial) string tension and it has the functional form one would expect if the vortices being studied were responsible for the confinement at low T, and for the `spatial' confinement at large T. We also discuss in detail some of the direct numerical evidence for a non-zero spatial string tension at high T, and we show that the observed linearity of the (spatial) potential extends over distances that are large compared to typical high-T length scales.

gauge field theory: SU(2)
lattice field theory
dimension: 3
vortex
confinement
finite temperature
string tension
boundary condition
domain wall
numerical calculations: Monte Carlo

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