String effects in Polyakov loop correlators

TL;DR

This work tests the effective string description of confinement in finite-temperature gauge theories by analyzing Polyakov-loop correlators in the three-dimensional $\mathbb{Z}_2$ model. It shows that the free bosonic string accurately describes fluctuations at sufficiently low temperatures and long distances ($T\le T_c/3$), while near the deconfinement region the self-interactions of the string are essential; incorporating next-to-leading order Nambu-Goto corrections yields excellent agreement up to $T\sim T_c/2$ without new parameters. The findings, supported by high-precision Monte Carlo data, reinforce the universality of the effective string picture for confining flux tubes in gauge theories. The results have implications for understanding confinement and flux-tube dynamics in more complex gauge theories, including $SU(N)$ cases in $2+1$ and $3+1$ dimensions.

Abstract

We compare the predictions of the effective string description of confinement in finite temperature gauge theories to high precision Monte Carlo data for the three-dimensional Z_2 gauge theory. First we review the predictions of the free bosonic string model and their asymptotic behavior in the various regimes of physical interest. Then we show that very good agreement with the Monte Carlo data is obtained, for temperatures not too close to the deconfinement one (typically T<T_c/3). For higher temperatures, higher order effects are not negligible: we show that they are accurately modeled by assuming a Nambu-Goto string action and computing its partition function at next-to-leading order.

Figures (4)

• Figure 1: Comparison between free string prediction and Monte Carlo data for $Q_q(R)$ as defined in Eq.(\ref{['Qq']}). The Monte Carlo data are taken at $\beta=0.73107$ and $T=T_c/3=(12 a)^{-1}$, and are plotted as a function of $z=2R/L$. The solid line is the prediction Eq.(\ref{['Qqfree']}) for this quantity. The dashed line is the asymptotic value $-\pi/6L$ of the free string prediction for large $z$.
• Figure 2: Same as Fig. 1 for $\beta=0.74603$ and $T=T_c/3=(18 a)^{-1}$
• Figure 3: Data for $Q_q$ at $\beta=0.73107$ and $T=T_c/2=(8 a)^{-1}$. The solid line is the full NLO string prediction, while the dash-dotted line is the free string prediction.
• Figure 4: Same as Fig. 4 for $\beta=0.74603$ and $T=T_c/2=(12 a)^{-1}$