On the color structure of Yang-Mills theory with static sources in a periodic box

TL;DR

This study explores the color structure of the wave functionals in SU(3) Yang-Mills theory with static quark-antiquark pairs, confirming that only color singlet states contribute to the lowest energy states in a periodic box.

Contribution

It provides numerical evidence that all states contributing to the Feynman kernel are global color singlets and compares different boundary conditions to analyze their effects.

Findings

All contributing states are global color singlets.

Lowest energies in singlet and octet sectors agree within errors.

Octet correlator is compatible with zero under certain boundary conditions.

Abstract

We present an exploratory numerical study on the lattice of the color structure of the wave functionals of the SU(3) Yang-Mills theory in the presence of a $q\bar q$ static pair. In a spatial box with periodic boundary conditions we discuss the fact that all states contributing to the Feynman propagation kernel are global color singlets. We confirm this numerically by computing the correlations of gauge-fixed Polyakov lines with color-twisted boundary conditions in the time direction. The values of the lowest energies in the color singlet and octet external source sectors agree within statistical errors, confirming that both channels contribute to the lowest (global singlet) state of the Feynman kernel. We then study the case of homogeneous boundary conditions in the time direction for which the gauge-fixing is not needed. In this case the lowest energies extracted in the singlet external source sector agree with those determined with periodic boundary conditions, while in the octet sector the correlator is compatible with being null within our statistical errors. Therefore consistently only the singlet external source contribution has a non-vanishing overlap with the null-field wave functional.