[Paper Review] Quantum delocalization of strings with boundary action in Yang-Mills theory

Ahmed S. Bakry, M. Deliyergiyev+3 more|arXiv (Cornell University)|Jan 8, 2020

Black Holes and Theoretical Physics117 references4 citations

TL;DR

This paper investigates quantum delocalization of QCD flux tubes in 4D SU(3) Yang-Mills theory near the deconfinement transition using lattice Monte Carlo data. By extending the Lüscher-Weisz string action with Lorentz-invariant boundary terms and rigidity corrections beyond the Nambu-Goto approximation, the model achieves a significantly improved fit to the width profile of the flux tube across 0.5–1.2 fm, especially at high temperatures, demonstrating that rigidity and boundary symmetry effects are essential for accurate description of non-perturbative string dynamics.

ABSTRACT

The width of the quantum delocalization of the QCD strings is investigated in effective string models beyond free Nambu-Goto approximation. We consider two Lorentzian-invariant boundary-terms in the Lüscher-Weisz string action in addition to self-interaction term equivalent to two loop order in the (NG) string action. The geometrical terms which realize the possible rigidity of the QCD string is scrutinized as well. We perform the numerical analysis on the 4-dim pure $SU(3)$ Yang-Mills lattice gauge theory at two temperature scales near deconfinement point. The comparative study with this QCD string model targets the width of the energy profile of a static quark-antiquark system for color sources separation $0.5 \le R \le 1.2$ fm. We find the inclusion of rigidity properties and symmetry effects of the boundary action into the string paradigm to reproduce a good match with the profile of the Mont-Carlo data of QCD flux-tube on this distance scale.

Motivation & Objective

• To address discrepancies between free Nambu-Goto string models and lattice Monte Carlo data for QCD flux-tube width near the deconfinement point.
• To investigate the role of boundary symmetries and rigidity in refining effective string models beyond the free Nambu-Goto approximation.
• To determine whether higher-order corrections in extrinsic curvature and boundary terms improve agreement with numerical data for the energy profile width in SU(3) Yang-Mills theory.
• To assess the validity of the Nambu-Goto action and its extensions in capturing the quantum delocalization of flux tubes at intermediate and short distances.

Proposed method

• Employing the Lüscher-Weisz effective string action with two Lorentz-invariant boundary terms to model edge effects in the flux tube.
• Including a self-interaction term equivalent to two-loop order in the Nambu-Goto action to account for quantum corrections.
• Introducing geometrical rigidity terms that suppress sharp fluctuations and model resistance to bending in the string.
• Performing numerical simulations on 4D pure SU(3) Yang-Mills lattice gauge theory at two temperatures near Tc: T/Tc = 0.8 and T/Tc = 0.9.
• Comparing the predicted width profiles of the flux tube with Monte Carlo data extracted from lattice simulations across R ∈ [0.5, 1.2] fm.
• Using χ²/dof minimization to evaluate the fit quality of different model variants, including free NG, NLO self-interaction, and rigid + boundary-corrected models.

Experimental results

Research questions

• RQ1 Does the inclusion of boundary symmetry effects and rigidity in the string action improve the fit to lattice Monte Carlo data for the flux-tube width?
• RQ2 How do the width profiles of the flux tube evolve with temperature, particularly near the deconfinement transition?
• RQ3 Can higher-order corrections in extrinsic curvature and boundary terms explain deviations from free string behavior at short distances?
• RQ4 Is the Nambu-Goto action sufficient to describe the quantum delocalization of QCD strings, or are additional physical effects like rigidity necessary?
• RQ5 What is the quantitative impact of rigidity and boundary terms on the χ²/dof and the rigidity parameter in the effective string model?

Key findings

• The inclusion of both boundary terms and rigidity effects in the string model reduces χ²/dof to 10.58/6 for R ∈ [0.5, 1.2] fm, indicating a significantly improved fit to lattice data.
• The next-to-leading-order (NLO) boundary term W²_{b4} provides a good match with lattice data down to R = 0.4 fm, suggesting relevance at short distances.
• Rigidity effects are found to be crucial for accurately reproducing the width profile near the deconfinement point, especially at T/Tc = 0.9, where free string models fail.
• The fit using both boundary and rigidity corrections shows a 20–30% change in the rigidity parameter compared to the NLO approximation, indicating non-trivial sensitivity to model structure.
• At T/Tc = 0.8, the constant width profile across all distances is consistent with the pure Nambu-Goto action, suggesting thermal effects fade out and the string behavior becomes more stable.
• The self-interaction term in the NLO expansion flattens the width profile in the intermediate region, counteracting the curved profile of the free string, and improves consistency with lattice data.