Holonomy potential and confinement from a simple model of the gauge topology

TL;DR

The paper addresses the origin of the finite-temperature holonomy potential that drives confinement in pure SU(2) gauge theory by modeling an ensemble of instanton-dyons with excluded-volume repulsion. It fixes dyon densities from lattice-calculated caloron data and derives an effective holonomy potential $V_{eff}$ that includes a perturbative piece, showing that sufficiently strong dyon repulsion can induce confinement near $T_c$. The authors compute electric and magnetic screening masses and dyon densities from $V_{eff}$ and demonstrate qualitative agreement with lattice data, while offering concrete predictions for dyons that await further lattice verification. This work provides a gauge-topology–based mechanism for confinement and lays groundwork for extensions to QCD with fermions and potential Monte Carlo tests.

Abstract

We discuss an ensemble of topological solitons -- instanton-dyons and antidyons - in SU(2) pure gauge theory at finite temperatures above and below the deconfinement phase transition temperature. The main focus is on the combined effect of this ensemble on the so called effective holonomy potential, which drives the confinement/deconfinement phase transition. Using a simple model with excluded volume and lattice data on caloron density we find that repulsive part of the potential is robust enough to induce the phase transition at the right temperature. Model's predictions -- the holonomy potential, electric and magnetic screening masses as a function of T -- are in qualitative agreement with the available lattice data. Further predictions are densities of various dyon types as a function of temperature: while some lattice measurements of them had been made, much more accurate data are needed to test these predictions.

Figures (3)

• Figure 1: Caloron density as a function of $T/T_c$. The solid curve is the semiclassical fit $n_{\text{cal}}=K S_{cal}^2 e^{-S_{cal}}$ in units of $T$ with parameters $K=0.024$, $S_{cal}=8\pi^2/g^2(T)$, open (filled) points are the lattice data from Ilgenfritz:2006ju (Bornyakov:2008im).
• Figure 2: The upper plot shows the effective potential $V_{eft}(b)/T$\ref{['eq:potential']} for $T/T_c=0.8,1,1.5$ shown by the dashed,solid and dot-dashed lines, respectively. The plot shows electric $m_E/T$ and magnetic $m_M/T$ screening masses versus temperature, indicated by the solid and dashed lines, respectively. Thick lines are our model, the data points are from lattice propagators Bornyakov:2010nc, the lines connecting data points are shown simply for their identification.
• Figure 3: Prediction of the model for the temperature dependence of the density of the instanton-dyons are shown by the lines, those with solid and dashed lines are for $M,L$ type dyons, respectively. Open (filled) circles show identified $M$-type dyons from ref. Ilgenfritz:2006ju (Bornyakov:2008im). The crosses show "unidentified topological objects" from Ilgenfritz:2006ju. Circles and crosses provide the lower and the upper bound for the dyon density.