Confinement from correlated instanton-dyon ensembles in SU(2) Yang-Mills theory

We study the confinement phase transition in SU(2) Yang-Mills theory, based on a statistical ensemble model of correlated instanton-dyons. We show for the first time that such a model provides a quantitative description, in light of the lattice data, for the temperature dependence of the order parameter. We characterize the short-range interaction which plays a crucial role for the properties of such an ensemble. The chromomagnetic charge density as well as the spatial correlations are found to be consistent with known lattice and phenomenological information.

Figure 1

The holonomy potential $\mathcal{U}$ as a function of holonomy $L_{\infty }$ for different actions $S$ from larger to smaller values (from top to bottom), or equivalently from higher to lower temperatures. See text for details.

Figure 2

The Polyakov loop expectation value $⟨L_{\infty }⟩$ versus temperature $T/T_c$. The filled circle and diamond symbols are for lattice results [39, 40], while the open symbols are from instanton-dyon ensemble calculations with different choices of parameters. See text for details.

Figure 3

The density of chromomagnetic charges at different temperatures from the instanton-dyon ensemble, compared with lattice results from Ref. [44]. See text for details.