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Intrinsic Width of the flux tube in 2+1 dimensional Yang-Mills theories

Lorenzo Verzichelli, Michele Caselle, Elia Cellini, Alessandro Nada, Dario Panfalone

Abstract

We present our updated results on the intrinsic width of the profile of the flux tube in (2+1)-dimensional Yang-Mills theory with SU(2) gauge group. We identify the intrinsic width as the characteristic length scale of the exponentially decaying tails of the profile of the flux tube. Inspecting a broad range of temperature, we check that this length does not depend on the length of the flux tube. Our estimations of the intrinsic width show a constant value at low temperature and a growing trend approaching the deconfinement temperature that can be understood from the universality class of the phase transition via the Svetitsky-Yaffe mapping.

Intrinsic Width of the flux tube in 2+1 dimensional Yang-Mills theories

Abstract

We present our updated results on the intrinsic width of the profile of the flux tube in (2+1)-dimensional Yang-Mills theory with SU(2) gauge group. We identify the intrinsic width as the characteristic length scale of the exponentially decaying tails of the profile of the flux tube. Inspecting a broad range of temperature, we check that this length does not depend on the length of the flux tube. Our estimations of the intrinsic width show a constant value at low temperature and a growing trend approaching the deconfinement temperature that can be understood from the universality class of the phase transition via the Svetitsky-Yaffe mapping.
Paper Structure (5 sections, 12 equations, 5 figures, 1 table)

This paper contains 5 sections, 12 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Lattice Setup
  3. Low Temperature Results
  4. High Temperature Results
  5. Conclusions

Figures (5)

  • Figure 1: Schematic representation of the three point function $F_{01}(R, y)$.
  • Figure 2: Values of $\lambda$ obtained from the fit using the Clem formula as a model. In both panels the horizontal axis is the length of the flux tube. In the left panel we plotted results from different lattice spacings keeping the temperature constant at $T = 0.23 \, T_c$; in the right one we fixed $\beta = 10.865$ and varied the temperature. The solid line and the shaded band represent our final results and its uncertainty.
  • Figure 3: The effective width as a function of the length of the flux tube. The dashed line is the logarithmic broadening expected from effective string theory predictions. The coefficient was fixed to the predicted value, while the vertical offset was fitted to the data.
  • Figure 4: Square of the total width from the fit assuming the SY mapping of our data at $T = 0.68 \, T_c$. The dashed line with the confidence band is the expansion from Eq. \ref{['eq:SY_linearbroad']}. The input value of $\lambda$ is the one extracted from the Polyakov loop correlator $\lambda = 1 / (2 E_0)$.
  • Figure 5: The values of $\lambda$ as a function of the temperature. The red dash-dotted line is our estimation at low temperature. The black solid line is the SY prediction, using the fit from Ref. Caselle:2024zoh for $E_0$.