Volker Weinberg

Exploring the structure of the quenched QCD vacuum with overlap fermions

Overlap fermions have an exact chiral symmetry on the lattice and are thus an appropriate tool for investigating the chiral and topological structure of the QCD vacuum. We study various chiral and topological aspects of quenched gauge field configurations. This includes the localization and chiral properties of the eigenmodes, the local structure of the ultraviolet-filtered field strength tensor, as well as the structure of topological charge fluctuations. We conclude that the vacuum has a multifractal structure.

The QCD vacuum probed by overlap fermions

We summarize different uses of the eigenmodes of the Neuberger overlap operator for the analysis of the QCD vacuum, here applied to quenched configurations simulated by means of the Luscher-Weisz action. We describe the localization and chiral properties of the lowest modes. The overlap-based topological charge density (with and without UV-filtering) is compared with the results of UV-filtering for the field strength tensor. The latter allows to identify domains of good (anti-)selfduality. All these techniques together lead to a dual picture of the vacuum, unifying the infrared instanton picture with the presence of singular defects co-existent at different scales.

Topological Structure of the QCD Vacuum Revealed by Overlap Fermions

Overlap fermions preserve a remnant of chiral symmetry on the lattice. They are a powerful tool to investigate the topological structure of the vacuum of Yang-Mills theory and full QCD. Recent results concerning the localization of topological charge and the localization and local chirality of the overlap eigenmodes are reported. The charge distribution is radically different, if a spectral cut-off for the Dirac eigenmodes is applied. The density q(x) is changing from the scale-a charge density (with full lattice resolution) to the ultraviolet filtered charge density. The scale-a density, computed on the Linux cluster of LRZ, has a singular, sign-coherent global structure of co-dimension 1 first described by the Kentucky group. We stress, however, the cluster properties of the UV filtered topological density resembling the instanton picture. The spectral cut-off can be mapped to a bosonic smearing procedure. The UV filtered field strength reveals a high degree of (anti)selfduality at “hot spots” of the action. The fermionic eigenmodes show a high degree of local chirality. The lowest modes are seen to be localized in low-dimensional space-time regions.

Momentum dependence of the topological susceptibility with overlap fermions

Knowledge of the derivative of the topological susceptibility at zero momentum is important for assessing the validity of the Witten-Veneziano formula for the η 0 mass, and likewise for the resolution of the EMC proton spin problem. We investigate the momentum dependence of the topological susceptibility and its derivative at zero momentum using overlap fermions in quenched lattice QCD simulations. We expose the role of the low-lying Dirac eigenmodes for the topological charge density, and find a negative value for the derivati ve. While the sign of the derivative is consistent with the QCD sum rule for pure Yang-Mills theory, the absolute value is overestimated if the contribution from higher eigenmodes is ignored.

Vacuum structure as seen by overlap fermions

Three complementary views on the QCD vacuum structure, all based on eigenmodes of the overlap operator, are reported in their interrelation: (i) spectral density, localization and chiral properties of the modes, (ii) the possibility of filtering the field strength with the aim to detect selfdual and antiselfdual domains and (iii) the various faces of the topological charge density, with and without a cutoff \lambda_{\rm cut} = O(\Lambda_{QCD}). The techniques are tested on quenched SU(3) configurations.