YM-Thermodynamics 2024, 37: Decay of the Preconfining Ground State

Closed lines of magnetic flux form along regions where dissociation of large-holonomy (anti)calorons is characterized by a net direction as discussed in the previous segment. In the preconfinig phase, vortex loops are unresolved and short-lived due to the curvature of the vortex line inducing a motion along the normal to the vortex line, which causes the loop to shrink, and eventually collapse. No condensate of vortex loops (n = 0) forms discrete magnetic center symmetries Zn for SU(n), unbroken in the preconfining phase. In the confining phase magnetic center transformations are induced by singular gauge transformations of the dual gauge field along closed spatial contours. The electric center symmetry is restored when temperature drops below critical, and the Polyakov-loop expectation doesn't apply anymore. The condensation of center-vortex loops with n = 0 is due to the masslessness and quasistability. They qualify as constituents of a new ground state, characterized by a complex and scalar field. The condensation has discrete degeneracy with respect to the phase, signaling the dynamical breaking of the magnetic center symmetries. The emergence of the field stems from the t'Hooft-loop operator as the exponential of the magnetic flux of the dual gauge field through the minimal surface, spanned by an oriented, closed spatial curve centered at some point. The expectation value of the field changes phase in discrete steps under singular gauge transformation along the chosen contour.

Given a spatial circle with infinite radius centered on some point, the thermally averaged flux through a manifold of a center-vortex loop is given by

The way this is evaluated depends on whether the manifold is pierced an even/odd number of times by the flux lines.

The decay of the (anti)monopole condensates and the formation of the center-vortex condensate are described by real-time dynamics of the scalar and complex order-parameter of the field for the dynamical breakdown of the magnetic center symmetry.

Nonvanishing, selfintersection-number n center-vortex loops can form during the relaxation of the field to one of the center-degenerate minima of the potential V. This is associated with a stable condensate originating from paired, magnetic center-vortex loops with n = 0. The 2-fold directional degeneracy are interpreted as massless or massive spin-1/2 fermions. In SU(2), fermionic solitons generated in the course of the process of turning a (anti)monopole condensate into a condensate of massless, pointlike, and interaction-free center-vortex-loops are primarily classified by their topology relating to the selfintersection-number. At finite mass, contact interactions occur only due to the complete decoupling of propagating gauge modes in the confining phase. At multiplicity Mₙ for n selfintersections and naked mass nΛ,