YM-Thermodynamics 2024, 32: Further Features of Wilson Loops

A good separation doesn't take place in deconfining SU(2) YM-Thermodynamics, but there is an essential feature implying an area law for the contributions of the unscreened magnetic fluxes by (anti-)monopoles adjacent to the surface spanned by the quadratic spatial contour of the side-length. The length scale determines the slab of thickness containing magnetic quasiparticles, which are contained in the slab responsible for the flux. Exponentiate the normalized flux of a single (anti-)monopole through the minimal surface spanned by the quadratic contour in the infinite limit of the side-length, by a magnetic charge, which can be made explicit by the usage of the probability P(l)

In effective variables, the spatial Wilson loop in the gauge-field variables of the effective theory for the deconfining phase of SU(2) YM-Thermodynamics can be computed explicitly. It first must be associated with some finite resolution, which is generally different from the definition emerging directly from the fundamental variables. At finite temperatures, the deconfining phase of the YM-theory, only one resolution scale is valid: μ = |ϕ|. Intuitively, the spatial Wilson loop might be evaluated on propagating, radiatively dressed gauge modes, so that the magnetic flux in the effective theory measures the average flux sourced by the ensemble of magnetic monopoles, and as previously, the resummation over the one-loop polarization tensor of the TLM mode should suffice.

The massive contribution of the V-propagators to the Wilson loop is acquired by summing over the contributions.

For the massless mode, replace the mass with the screening function Gτ². Extending this to the vacuum,