Evidence of instanton effects in hadrons from the study of low eigenfunctions of the Dirac operator

Testing the self-duality of topological lumps in SU(3) lattice gauge theory

We discuss a simple formula which connects the field-strength tensor to a spectral sum over certain quadratic forms of the eigenvectors of the lattice Dirac operator. We analyze these terms for the near zero modes and find that they give rise to contributions which are essentially either self-dual or anti-self-dual. Modes with larger eigenvalues in the bulk of the spectrum are more dominated by quantum fluctuations and are less (anti-)self-dual. In the high temperature phase of QCD we find considerably reduced (anti-)self-duality for the modes near the edge of the spectral gap.

Meron pairs and fermion zero modes

Merons, conjectured as a semiclassical mechanism for color confinement in QCD, have been described analytically by either infinite action configurations or an Ansatz with discontinuous action. We construct a smooth, finite action, stationary lattice solution corresponding to a meron pair. We also derive an analytical solution for the zero mode of the meron pair Ansatz, show that it has the qualitative behavior of the exact zero mode of the lattice solution, and propose the use of zero modes to identify meron gauge field configurations in stochastic evaluations of the lattice QCD path integral.