Particle theory

Abstract:

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 T < Tc this observation is consistent with the fact that the phase is linearly confining; while for T > Tc 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.

Abstract:

We calculate the euclidean action of a pair of ℤ2 monopoles (instantons), as a function of their spatial separation, in D = 2 + 1 SU(2) lattice gauge theory. We do so both above and below the deconfining transition at T = Tc. At high T, and at large separation, we find that the monopole "interaction" grows linearly with distance: the flux between the monopoles forms a flux tube (exactly like a finite portion of a ℤ2 domain wall) so that the monopoles are linearly confined. At short distances the interaction is well described by a Coulomb interaction with, at most, a very small screening mass, possibly equal to the Debye electric screening mass. At low T the interaction can be described by a simple screened Coulomb (i.e. Yukawa) interaction with a screening mass that can be interpreted as the mass of a "constituent gluon". None of this is unexpected, but it helps to resolve some apparent controversies in the recent literature.