Silvano Petrarca

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 $q\overline{q}$ 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 nonvanishing overlap with the null-field wave functional.

We report on a precise computation of the topological charge distribution in the SU(3) Yang-Mills theory. It is carried out on the lattice with high statistics Monte Carlo simulations by employing the definition of the topological charge suggested by Neuberger’s fermions. We observe significant deviations from a Gaussian distribution. Our results disfavor the $\theta$ behavior of the vacuum energy predicted by dilute instanton models, while they are compatible with the expectation from the large $N_c$ expansion.