Width of the confining string in Yang-Mills theory

Area of Science:

• High Energy Physics
• Quantum Field Theory
• Lattice Gauge Theory

Background:

• Understanding the nature of quark confinement is crucial in quantum chromodynamics.
• The behavior of the flux tube (confining string) between static quarks provides insights into non-perturbative aspects of gauge theories.
• Previous studies have explored string properties, but precise calculations of transverse fluctuations remain challenging.

Purpose of the Study:

• To investigate the transverse fluctuations of the confining string in (2+1)D SU(2) Yang-Mills theory.
• To determine how the string width depends on the distance between static quarks.
• To compare numerical results with analytical predictions from effective string models.

Main Methods:

• Utilizing Monte Carlo simulations to model the (2+1)D SU(2) Yang-Mills theory.
• Employing an efficient multilevel algorithm to extract the exponentially suppressed signal from noise.
• Performing analytical calculations of higher-order corrections to the effective string action.

Main Results:

• The width of the confining string exhibits a logarithmic increase with the separation distance between static quarks.
• Numerical data for the string width were accurately fitted by analytical calculations, including higher-order corrections.
• The study successfully extracted a weak signal from significant noise using a specialized algorithm.

Conclusions:

• The transverse fluctuations of the confining string in (2+1)D SU(2) Yang-Mills theory show a clear logarithmic dependence on quark separation.
• Analytical predictions derived from effective string models, incorporating higher-order terms, provide an accurate description of the numerical findings.
• The employed multilevel algorithm demonstrates high efficiency in analyzing noisy lattice gauge theory data.