Intrinsic Width of the Flux Tube as a tool to explore confining mechanisms in Lattice Gauge Theories

Abstract

We study the profile of the flux tube in the SU(2) gauge model in (2 + 1) dimensions, with a particular attention to the so called "intrinsic width" which drives the exponential decay of the flux density at large transverse distances and represents a new physical scale of the model. This quantity is directly related to the confining mechanism which generates the flux tube and can be used to test its properties. We study a wide range of different values of lattice spacing, temperature and flux tube lengths and show that our data are precise enough to distinguish between different confining models. In particular we show that at high temperatures (just below the deconfinement transition) the data are perfectly described by an Ising-like effective model based on the Svetitsky-Yaffe mapping. At lower temperatures this approximation does not hold anymore. In this regime (which is the most interesting one from a physical point of view) we test several alternative proposals and show that the dual superconductor model is the one which better fits the data. However, this proposal is not fully satisfactory, because the values of the Ginzburg-Landau parameter extracted from the fits increase with the length of the flux tube, which is not a feature predicted by the model. This suggests that a more sophisticated model is needed to explain confinement in non-abelian gauge theories and, at the same time, that our data on the intrinsic width may be a powerful tool to benchmark these candidates.

Figures (12)

• Figure 1: Schematic representation of the three-point function $F_{\mu \nu}$ in Eq. \ref{['eq:three_pts']}, with $\hat{\mu} = \hat{0}$ and $\hat{\nu} = \hat{1}$. Thick lines indicate the traced Wilson lines: the two Polyakov loops (red, blue) and the plaquette operator (black).
• Figure 2: The profile of the flux tube for fixed lattice spacing and different temperature $T$ (left panel) and vice versa (right panel). Note that, in order to compare between different values of the lattice spacing, the profile has been rescaled with the square of the string tension. The profiles obtained with $\beta = 10.865$ (left panel) correspond to $R = 9 \, a = 1.18 / \sqrt{\sigma}$, while for the one at $\beta=12.963$ the distance was set to $R = 11 \, a = 1.20 / \sqrt{\sigma}$.
• Figure 3: Comparison of the profile from a simulation of the $(2+1)$-dimensional $\mathop{\mathrm{\mathrm{SU}}}\nolimits(2)$ gauge theory (at $\beta = 10.865$) with one from direct simulation of the Nambu-Got=o EST. In both cases, the length of the string equals $9a$ and the temporal extent is $60a$.
• Figure 4: Example of spline interpolation of the Gaussian peak (solid black line) and exponential fit of the tails (red dash-dotted line). The profile was obtained from the simulation at $\beta = 10.865$ and $T = 0.23 \, T_c$, with $R = 11 a$.
• Figure 5: Example of a fit with the Clem model, see Eq. \ref{['eq:clem']}, for a profile obtained at $\beta = 10.865$ and $T = 0.23 \, T_c$, with $R = 11 a$.