Hedgehogs in Wilson loops and phase transition in SU(2) Yang-Mills theory

TL;DR

This paper introduces gauge-invariant hedgehog-like structures in Wilson loops as physically relevant degrees of freedom in SU(2) Yang-Mills theory, showing their density correlates with the finite-temperature phase transition.

Contribution

It demonstrates that hedgehog line density in Wilson loops acts as an order parameter for the deconfinement transition in SU(2) Yang-Mills theory.

Findings

Hedgehog line density is insensitive to temperature in the confinement phase.

Density changes significantly across the deconfinement transition.

Hedgehog lines may influence quark-gluon plasma evolution in heavy-ion collisions.

Abstract

We suggest that the gauge-invariant hedgehoglike structures in the Wilson loops are physically interesting degrees of freedom in the Yang--Mills theory. The trajectories of these ``hedgehog loops'' are closed curves corresponding to center-valued (untraced) Wilson loops and are characterized by the center charge and winding number. We show numerically in the SU(2) Yang--Mills theory that the density of hedgehog structures in the thermal Wilson--Polyakov line is very sensitive to the finite-temperature phase transition. The (additively normalized) hedgehog line density behaves like an order parameter: the density is almost independent of the temperature in the confinement phase and changes substantially as the system enters the deconfinement phase. In particular, our results suggest that the (static) hedgehog lines may be relevant degrees of freedom around the deconfinement transition and thus affect evolution of the quark-gluon plasma in high-energy heavy-ion collisions.